Abstracts of light-front papers (1949-1991)

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Forms of relativistic dynamics: P.A.M. Dirac, Rev. Mod. Phys., 21, 392 (1949). Abstract For the purposes of atomic theory it is necessary to combine the restricted principle of relativity with the Hamiltonian formulation of dynamics. This combination leads to the appearance of ten fundamental quantities for each dynamical system, namely the total energy, the total momentum and the six vector which has three components equal to the total angular momentum. The usual form of dynamics expresses everything in terms of dynamical variables at one instant of time, which results in specially simple expressions for six of these ten, namely the momentum and the angular momentum. There are other forms for relativistic dynamics for which others of the ten are specially simple, corresponding to various sub-groups of the inhomogeneous Lorentz group. These forms are investigated and applied to a system of particles in interaction and to the electromagnetic field.
Renormalization effects for partially conserved currents: S. Fubini and G. Furlan, Physics, 1, 229 (1964).
Dynamics at infinite momentum: S. Weinberg, Phys. Rev., 150, 1313 (1966). Abstract Old-fashioned perturbation theory is applied to a relativistic theory in a reference frame with infinite total momentum. It is found that many undesirable diagrams disappear. The contribution of the remaining diagrams is described by a new set of rules with properties intermediate between those of Feynman diagram and old fashioned diagrams, e.g., energy denominators become covariant, and Feynman parameters appear naturally. The new rules are used to derive some integral equations.
Spin independence, spin, parity, and symmetry: H. Lipkin and S. Meshkov, Phys. Rev. 143, 1269 (1966). Abstract The assumption of strict spin independence of strong interactions between elementary particles forbids all three-meson and meson-baryon-baryon couplings, such as , , and . It is shown that these catastrophies may be avoided, even in the nonrelativistic limit, by adopting a modified definition of spin independence, i.e., W-spin independence. A nonrelativistic definition of W spin is obtained which requires only a trivial change to yield the relativistic description. The consequences of the assumption of W-spin independence are explored.
Representation of local current algebra at infinite momentum: R. Dashen and M. Gell-Mann, Phys. Rev. Lett. 17, 340 (1966).
Current algebras at infinite momentum: F. Coester and G. Roepstorff, Phys. Rev. 155, 1583 (1967). Abstract We examine the mathematical properties of the ``infinite-momentum limit'' of current-density operators. Free-field currents are examined for heuristic purposes. For physical particles we consider the restrictions of the current-density operators to the one-particle subspace. The existence of an operator limit is demonstrated for scalars, vectors, and antisymmetric tensors. The limit vanishes for scalars and, except in special cases, diverges for higher tensors. The kernels of the limit operators are obtained explicitly as functions of the same invariant form factors that determine the kernels of the original current densities. Commutation relations for the integrated currents are dynamical hypotheses. ``Local'' commutation relations for the densities of infinite momentum are incompatible with the assumption that the spins are bounded in the one-particle subspace.
Models of self-induced strong interactions: L. Susskind, Phys. Rev. 165, 1535 (1968). Abstract It is postulated that the theory of self-induced strong interaction possesses an infinite momentum limit. This limit is defined and its consequences are examined. It is found that some important simplifications occur if the limit exists. The limiting form of the theory is shown to have Galilean invariance with respect to motion transverse to the direction in which momentum is infinite.
Saturation of the isospin-factored current algebra at infinite momentum: S.J. Chang, R.F. Dashen, and L. O'Raifeartaigh, Phys. Rev. Lett. 21, 1026 (1968). Abstract The angular conditions for the isospin-factored current algebra at infinite momentum are decomposed into a set of momentum-transfer-independent conditions. The solutions to the angular conditions are constructed and related to wave equations. The existence of spacelike solutions is established for any nontrivial solution, and the decoupling problem is discussed.
in an infinite-momentum basis and the calculation of form factors: S.J. Chang, J.G. Kuriyan, and L. O'Raifeartaigh, Phys. Rev. 169, 1275 (1968). Abstract In the infinite-momentum limit the subgroup of the homogeneous Lorentz group becomes meaningful. It is shown that this decomposition of in an basis is also useful in calculations of form factors involving the group. In particular, the Barut-Kleinert and Nambu form factors are derived in a straightforward fashion.
Theories at infinite momentum: K. Bardacki and M.B. Halpern, Phys. Rev., 176, 1686 (1968). Abstract We construct Galilean invariant theories (with Schrodinger equation) at infinite momentum that describe interacting relativistic systems. Classes of both first- and second-quantized theories are presented. The formalism provides a general approach to the saturation of current algebra; positivity of the mass spectrum is guaranteed, and as much inelasticity as necessary may be introduced. More generally, however, such theories offer the hope of potential-theoretic intuition for relativistic physics.
Current algebra and lightlike charges: H. Leutwyler, Ed. G. Höhler, Springer Tracts in Modern Physics, Vol. 50 (1969).
Feynman rules and Quantum Electrodynamics at infinite momentum: S.-J. Chang and S.-K. Ma, Phys. Rev. 180, 1506 (1969). Abstract We have studied the Feynman rules in terms of the new variables and in the model and in quantum electrodynamics. The connection between the new variables and the dynamics at infinite momentum is established. In the model, one easily deduces Weinberg's rules at infinite momentum upon integrating over the s variables in the propagators without taking the limit. The new Feynman rules lead to much simpler calculation of the second order self-energies and the magnetic moment in QED. It is still unclear if there is advantage in computing higher-order terms in QED with the new rules.
Infinite momentum frames and particle dynamics: L. Susskind, in Lectures in Theoretical Physics, Vol. Xi-D, eds. K. T. Mahanthappa and E. E. Brittin, Gordon and Breach Science Publishers, New York, p. 135, (1969).
Infinite momentum limit of spinor field theory: D. Flory, Phys. Rev. 186, 1701 (1969). Abstract Weinberg has shown that in an infinite momentum frame moving along the - z axis, the old fashioned perturbation theory graphs containing intermediate particles with negative vanish. The result is here extended to a theory of spin- and scalar or pseudoscalar particles with a interaction ( or ) in a tree graph approximation. The effect of particles with a negative is absorbed into a counter term in the Hamiltonian. This counter term is of order in the coupling constant.
Momentum-transfer-independent angular relations and solutions to the isospin-factored current algebra: S.J. Chang, R. Dashen, and L. O'Raifeartaigh, Phys. Rev. 182, 1819 (1969). Abstract The main purpose of this paper is to construct a general class of solutions to the isospin-factored algebra of form factors at infinite momentum. Lorentz covariance imposes a very restrictive condition on these form factors, which is known as the angular condition. In this paper, we decompose this angular condition into a set of momentum-transfer-independent conditions. To further simplify our problem, we strengthen the angular conditions into three more restrictive and mutually exclusive classes of conditions (called primitive equations). These simplified angular conditions can be solved completely, and lead to three classes of primitive solutions. We find that for each of the primitive solutions there always exists an internal Lorentz group, and that these solutions are related to some very simple infinite-component wave equations. Having established the connection between the solution to the angular conditions and the wave equation, we then turn things around and construct some very general solutions from the coupled wave equations. The fact that these coupled equations represent the most general solutions to the primitive equations suggests that they may already represent the most general solution compatible with the original angular condition. Next, under very mild technical conditions, the solutions to the angular conditions are shown either to be physically trivial or to contain a spacelike () part. The possibility that the spacelike and timelike parts are not coupled by the currents is also discussed.
Multiphoton exchange amplitudes at infinite energy: S.J. Chang and S.K. Ma, Phys. Rev. 188, 2385 (1969). Abstract We illustrate in detail the summation of multiphoton exchange diagrams for ee, , and elastic scattering amplitudes at the high-energy limit using the infinite-momentum technique reported earlier. These diagrams are shown to give rise to amplitudes proportional to s, the center-of-mass energy squared, multiplied by simple combinations of the eikonal forms of high-energy scattering.
Properties of current algebra at infinite momentum: S.J. Chang, R. Dashen, and L. O'Raifeartaigh, Phys. Rev. 182, 1805 (1969). Abstract The sum rules of current algebra at infinite momentum can be considered as a system of coupled matrix equations, which we call the algebra of form factors. In addition to the equations following from sum rules, the form factors must also satisfy a complicated kinematic relation known as the angular condition. Presumably, the set of all hadron states (including the continuum) provides the basis for a representation of the algebra of form factors in which the angular condition is satisfied. It was conjectured by Dashen and Gell-Mann that a much smaller set of states containing only stable and resonant hadrons might also provide a representation. If this is true, the algebra of form factors could be used to predict many properties of hadrons. In the following paper, we attack the problem of finding a representation in which the angular condition is satisfied and in which all states have the same isospin. We obtain a large class of solutions which we suspect, but have not been able to prove, actually includes all solutions. None of our solutions has a physically acceptable mass spectrum. One purpose of the present paper is to discuss, in the proper physical context, the implications of the above-mentioned result. We discuss the algebra of form factors and the angular condition in detail, stressing those features which are general and not restricted to particular solutions. It is shown, for example, how one can incorporate additional equations following from the commutators of time components of currents with space components. We then consider the special problem of finding representations where all states have the same isospin. The relevance of this problem in the program of Dashen and Gell-Mann is discussed in detail.
Special relativity and diagonal transformations: L. Parker and G.M. Schmieg, Amer. Jour. Phys. 38, 218 (1969). Abstract We discuss the form of the special Lorentz transformation, and the corresponding transformation of the electromagnetic field, in which the transformation matrix is diagonal. We derive the diagonal form of the special Lorentz transformation directly, in a simple way, and show that it is sometimes more convenient to apply than the algebraically equivalent conventional form of the transformation. The convenience is especially evident in deriving the linear Doppler effect, and the relativistic addition of more than two parallel velocities. By writing Maxwell's equations in terms of linear combinations of coordinates which have simple transformation properties, we arrive at the transformation equations of the Maxwell fields in a diagonal form, as well as at the plane wave solutions, in a natural manner. The derivations and applications described above should be of use in a course on relativity because of their simplicity and directness.
Unitary representations of in an basis: S.J. Chang and L. O'Raifeartaigh, Jour. Math. Phys. 10, 21 (1969). Abstract Starting from the functional representation of Gel'fand and Naimark, the unitary irreducible representations of are described in a basis of the subgroup , where is the subgroup of all matrices of the form , . Physically, this is the subgroup into which degenerates at infinite momentum and may be thought of as the 2-dimensional Euclidean group together with its dilations. Advantages to using the basis are: (1) It is convenient to calculate form factors; (2) the generators of are represented either multiplicatively or by first-order differential operators and are independent of the values of the Casimir operators; (3) the principal and supplementary series of are treated on the same footing and, in particular, have the same inner product; and (4) the transformation coefficients to the usual angular-momentum basis are related to Bessel functions. The is used to compute explicitly the finite matrix elements of an arbitrary Lorentz transformation and to investigate the structure of vector operators in unitary representation of .
A useful form of the Minkowski diagram: L. Parker and G.M. Schmieg, Amer. Jour. Phys. 38, 1298 (1970). Abstract We give a diagrammatic representation of the diagonal form of the special Lorentz transformation. The null coordinates are plotted along a single set of orthogonal axes. Special Lorentz transformations are then represented only by a change of scale along those orthogonal axes. This diagram, which we call a null coordinate diagram, and the Minkowski diagram are closely connected. To demonstrate the use of the null coordinate diagram, we apply it to the linear Doppler effect, time dilation, and Lorentz contraction.
Infinite momentum limit of a spinor field theory. II: D. Flory, Phys. Rev. D1, 2795 (1970). Abstract A self contained theory of Dirac fermions interacting with (pseudo-) scalar bosons at infinite momentum has been constructed. The fields are coupled with a interaction where or , depending on the parity of the boson. The theory is designed to give the correct relativistic dynamics when the space of intermediate states is restricted to those states which can be interpreted as the infinite momentum limit of sets of particles with finite momentum, that is, those states which correspond to the particle configurations observed in nature. The intermediate states which are eliminated are those containing particles moving away from the infinite momentum observer. The dynamical effects of these states is incorporated into a counter term in the Hamiltonian. The effect of this counter term is to produce a set of four-point vertices in the old fashioned Hamiltonian perturbation expansion. The perturbation theory rules for this model were described in an earlier paper. A general formalism for handling interactions at infinite momentum is presented here. It is used to derive the counter term model theory. A complete set of generators for the Poincare group in a basis appropriate to the infinite momentum is demonstrated. These generators satisfy the commutation algebra of the Poincare group, proving the relativistic invariance of the theory and its consistency.
Quantum electrodynamics in the infinite momentum: J.B. Kogut and D.E. Soper, Phys. Rev. D1, 2901 (1970). Abstract We examine the formal foundations of QED in the infinite momentum frame. We interpret the infinite momentum limit as the change of variables , thus avoiding limiting procedures. Starting from the Feynman rules, we derive a ordered perturbation expansion for the S-matrix. We then show how this expansion arises from a canonical formulation of the field theory in the infinite momentum frame. We feel that this approach should lead to convenient approximation schemes for electrodynamics at high energy.
Quantum field theory on lightlike slabs: H. Leutwyler, J.R. Klauder and L. Streit, Il Nuo. Cim. Vol. LXVIA, No.3 (1970) Abstract Restricting the support of relativistic quantum fields to lightlike hyperplanes (e.g. =const) we find examples of such fields to exist as well defined self adjoint operators with properties however that differ vastly from those fields on the usual space like surfaces. We show that on a lightlike hyperplane: 1) the free field algebra is irreducible (instead of abelian, and in contrast to what one would expect of data on a characteristic surface) and 2) fields with different masses become unitarily equivalent (whereas they are inequivalent on spacelike surfaces). Furthermore the field algebra restricted to the space-time slab between two parallel lightlike planes is always irreducible (while there are counterexamples for spacelike slabs). We establish this directly for generalized free fields and rederive it for Wightman fields in general.
Theory of Deep-Inelastic Lepton-Nucleus Scattering and Lepton Pair Annihilation Processes. II. Deep-Inelastic Electron Scattering: S. D. Drell, D. J. Levi and T.-M. Yan, Phys. Rev. D1, 1035 (1970). Abstract This is the second in a series of four papers devoted to a theoretical study based on canonical quantum field theory of the deep-inelastic lepton processes. In the present paper we perform detailed calculations leading to the limiting behaviour- or the ``parton model"- for deep-inelastic electron scattering. It follows from this work that the structure functions depend only on the ratio of energy to momentum transfer as conjectured by Bjorken on general grounds. To accomplish this derivation, it is necessary to introduce a transverse momentum cut off so that there exists an asymptotic region in which and can be made larger than the transverse momenta of all the virtual constituents or ``partons" of the proton that are involved. We also derive the ladder approximation for the leading contribuion, order by order in the strong interaction and to all orders in the coupling, to the asymptotic behaviour of these structure functions with increasing ratio of energy to momentum transfer. Finally, we draw and discuss the experimental implications.
Galilean invariance in the infinite momentum frame and the parton model: C. Bouchiat, P. Fayet and P. Meyer, Nucl. Phys. B34, 157 (1971). Abstract Field theory in the infinite momentum frame variables is used to derive the parton model, and to stress the implications of transverse Galilean and longitudinal Lorentz boost invariances. The elastic nucleon electromagnetic form factor and inelastic structure functions are expressed as density and correlation functions for partons in the transverse plane, in direct analogy with expressions of non-relativistic atomic physics. A connection is established between the transverse momentum cut-off and the dependence of the electromagnetic elastic form factor. The scaling law for the parton model is derived under conditions which appear in a rather transparent way. The corresponding sum rules are studied. A generalization of the Bjorken-Feynman scaling is obtained in the non-forward Compton scattering amplitude relevant to the two-photon correction in very high-energy electron-nucleon elastic scattering.
Massive quantum electrodynamics in the infinite momentum frame: D. E. Soper, Phys. Rev. D4, 1620 (1971). Abstract We extend an earlier canonical formulation of QED in the infinite momentum frame by replacing the photons with massive vector mesons. The structure of the theory remains nearly the same except that a new term appears in the infinite momentum Hamiltonian describing the emission of helicity-zero vector mesons with an amplitude proportional to the meson mass.
Null plane field theory: F. Rohrlich, Acta Physica Austriaca, Supp. VIII, 277-322 (1971).
Quantum electrodynamics at infinite momentum: Scattering from an external field: J.D. Bjorken, J.B. Kogut and D.E. Soper, Phys. Rev. D3, 1382, (1971). Abstract Using a formulation of quantum electrodynamics in the infinite momentum frame, we develop a theory to describe the scattering of energetic electrons or photons off an external field. A physical picture emerges which proves to be a realization of Feynman's `parton' ideas. In this picture the incoming electron is composed of bare constituents (the quanta of Schrodinger fields) which, at high laboratory energies, interact slowly with one another. Each bare constituent is scattered from the external field in a simple way and constituents again interact among themselves to form the final state. This fomalism is applied to elastic electron and photon scattering, bremsstrahlung and pair production, and deep inelastic electroproduction of lepton pairs, and the results of Cheng and Wu and others are recovered in a simple way. In these applications, perturbation theory is used to construct the wavefunctions of constituents in the initial and final states.
Quantum electrodynamics on null planes and application to lasers : R. A. Neville and F. Rohrlich, Phys. Rev. D3, 1692 (1971). Abstract The conventional formulation of quantum electrodynamics in which the system develops from one space-like hyperplane to the next is here replaced by one in which the developement proceeds over null hyperplanes. For detailed study a quantized electromagnetic field is chosen to interact with a quantized spin-0 particle field in an unquantized electromagnetic field as background. If the later is chosen to be a laser field, the interaction permits exact closed-form solutions (Volkov) and allows the construction of wave packets which cannot be done in the usual formulation. The perturbation solution of the S matrix is therfore conveniently based on the Furry picture. The null-plane formulation has various advantages. In particular, the gauge problem which causes difficulties in the usual theory is absent in the null-plane gauge chosen here. Since there are only two dynamically independent components of , the commutation relations, field equations, gauge conditions, and vacuum definition are all mutually consistent. A natural null plane gauge is used. Similarities and differences between this and the conventional theory are pointed out. As an application the Compton scattering of a charged particle with a laser beam is shown to lead to an intensity-dependent frequency shift. The controversy on this issue is settled here without divergent phase factors, because our wave-packet description permits a clean seperation of the particle beam from the laser.
Quantum field theory of null planes: R. A. Neville and F. Rohrlich, Il. Nuo Cimento Vol. 1A, No. 4, 625 (1971). Abstract The initial-value problem for hyperbolic differential equations with the initial data given on a null plane in Minkowski space is considered in detail for the KLein-Gordon and Dirac equations. Existence and uniqueness theorems are given. The quantum field theoretic analogue involves the commutation relations on the null plane and the null translation operator off that plane. The formal theory of interacting fields is stated briefly in the Feynman-Dyson spirit. It is pointed out that an interaction that involves the null co-ordinate derivative of the field in the direction off the initial plane leads to additional complications.
Canonical light-cone commutators and their applications: R. Jackiw, Springer Tracts in Modern Physics, 62 (1972).
Infinite-momentum helicity states: D. Soper, Phys. Rev. D5, 1956 (1972). Abstract We discuss and generalize to arbitrary spin the kind of single-particle spin states which have appeared naturally in field theories in the infinite-momentum frame. These states transform simply under the Galilean symmetry group which is important in the infinite-momentum frame, rather than under the rotation group. We also find that the spinors representing these states are very simple.
Validity of the infinite momentum frame canonical formalism for simple loop diagrams: C. Bouchiat, P. Fayet and N. Sourlas, Lett. al. Nuo Cimento, Vol. 4, No.1, 9 (1972).
Current and constituent quarks in the light-cone quantization: E. Eichten, F. Feinberg, and J. F. Willemsen, Phys. Rev. D8, 1204 (1973). Abstract Using the light-cone quantization of the free-quark model, a wide class of unitary transformations which relate the ``current" to the ``constituent" quark models is constructed. The Melosh transformation is obtained as a special case. The construction clearly exhibits the kinematical aspects of the transformation. Phenomenological applications are discussed. A method for determining acceptable transformations in potential models is formulated.
Quantization of the Yang-Mills field in the null-plane frame: E. Tomboulis, Phys. Rev. D8, 2736 (1973). Abstract The massless Yang-Mills field is quantized in the null frame gauge =0, and Feynman rules are derived.
Quantum electrodynamics and renormalization theory in the infinite momentum frame: S.J. Brodsky, R. Roskies and R. Suaya, Phys. Rev. D8, 4574 (1973). Abstract Time-ordered perturbation theory evaluated in the infinite momentum frame of Weinberg is shown to be a viable calculational alternative to the usual Feynman graph procedure for QED. We derive the rules of calculation at infinite momentum, and introduce convenient method for automatically including z graphs (backward moving fermion contributions). We then develop techniques for implementing renormalization theory, and apply these to various examples. We show the limit is uniform for calculating renormalized amplitudes, but this is not true in evaluating the renormalization constants themselves. Our rules are then applied to calculate the electron anomalous moment through fourth order and a representative diagram in sixth order. It is shown that our calculations are competitive with the normal Feynman approach in practical calculations. some implications of our results and connections with light-cone quantization are discussed.
Quantum field theories in the infinite momentum frame. I . Quantization of scalar and Dirac fields: S.-J. Chang, R.G. Root and T.-M. Yan, Phys. Rev. D7, 1133 (1973) Abstract Renormalized coupled scalar and Dirac fields are quanized in equal surfaces (called light fronts). Schwinger's action principle is employed to deduce the correct canonical equal (anti-) commutation relations. These theories are shown to be Lorentz invariant. Generalized Schwinger conditions for a quantum field theory to be Lorentz invariant are given and discussed in an appendix. Spectral sum rules are derived. Leading singularities of Green's functions and products of field operators near the light cone are studied and the implications to current algebra sum rules are discussed. We also discuss some of the delicate features of the light-front formalism.
Quantum field theories in the infinite momentum frame. II. Scattering matrices of scalar and Dirac fields: S.-J. Chang and T.-M. Yan, Phys. Rev. D7, 1147 (1973). Abstract The scattering matrices of field theories formulated in the light front quantization of the preceding paper are studied. Reduction formulas for scalar and Dirac particles are derived. The scattering matrices in this new formulation are shown to give the same predictions as in the equal time formulation to all orders in perturbations. Second-order renormalization is carried out and it gives well known results. New Feynman rules of the perturbation theory are given and their peculiarities are discussed.
Quantum field theories in the infinite momentum frame. III. Quantization of the coupled spin-one fields: T.-M. Yan, Phys. Rev. D7, 1760 (1973). Abstract Light front quantization of spin-one fields coupled to a conserved or nonconserved current constructed from a Dirac field is studied. It is shown that an operator field transformation must be performed on the Dirac field in order to maintain simple canonical commutation relations and a simple hamiltonian. In this formulation QED emerges as the zero mass limit of the massive gluon model. Lorentz invariance of the vector gluon model is explicitly verified. Vacuum expectation values of operator products and Green's functions are studied and spectral sum rules are derived. The general structure of the current commutators on a light fornt is formally not altered by the interactions. Feynman's parton model for deep inelastic scattering is derived from canonical light front current commutation relations. The structure function in the Bjorken scaling limit is related to the distribution of constituents of the hadron target in any frame of reference.
Quantum field theories in the infinite momentum frame. IV. Scattering matrix of vector and Dirac fields and perturbation theory: T.-M. Yan, Phys. Rev. D7, 1780 (1973) Abstract The scattering matrix of coupled spin-one and Dirac fields formulated in light front quantization of the preceding paper is studied. The scattering matrix of the vector gluon model in this new formulation is shown to give the same predictions as the equal time formulation to all orders in perturbation theory. Renormalizability of this model in the new formulation is also established. A further test of the light front quantization of spin one fields is discussed by examples of fermion-fermion interaction and virtual as well as real Compton scattering in the axial vector gluon model in the lowest order perturbation theory. A reduction formula for vector particles is derived and the Wick theorem is proved. Peculiarities in the perturbation theory of the light front formulation are discussed. Finally, a parton-like model for scattering of two energetic particles is proposed which satisfies manifest s-channel unitarity.
The parton picture of elementary particles: J. Kogut and L. Susskind, Phys. Rep. 8, 75 (1973). Abstract The parton theory is developed along several lines. We begin by developing quantum mechanics in the infinite momentum frame. The Galilean anology is worked out and the use of nonrelativistic reasoning in relativistic contexts is illustrated. Application of infinite momentum quantum mechanics includes the computation of the radius of a relativistic bound state, space time visualization of the multiperipheral model and the eikonal approach to high energy scattering. The classic phenomenological application of the parton model are reviewed and explained. These include deep inelastic electroproduction, the shrinking photon effect and heavy lepton pair production. The string model of the hadron is formulated in the infinite momentum frame as a parton model. We consider currents and the distribution of spins among the partons of the hadronic string. We suggest that it is profitable to view a hadron as a one dimensional lattice of spins and isospins and show that many of the properties of the lattice can be related to the meson spectrum. Application of the spin lattice ideas are made to deep inelastic electron and neutrino scattering. Predictions are made for the behaviour of the structure functions in these processes. Multiparticle production is examined in the string model. We derive the distribution of the secondaries in longitudinal and transverse momentum, the charge per secondary as a function of the rapidity and the correlations among the secondaries at different rapidities. Speculations are made about a class of phenomena which go beyond the string model. These phenomena we call the hadron parton effects. They include the production of large transverse momenta among secondaries, logarithmically increasing total cross sections and power behaviour of wide angle exclusive cross sections. We conclude with some speculations about the breakdown of the parton model.
Wick equation, the infinite momentum and perturbation theory: G. Feldman, T. Fulton and J. Townsend, Phys. Rev. D7, 1814 (1973). Abstract The eigen values of the Wick equation in the weak binding limit are found in perturbation theory employing two different approaches: (1) a covariant approach using an integral representation for the Bethe-Salpeter wave function and (2) quantization in the infinite momentum frame using technique of Kogut and Soper. The eigen values agree to order .
A two dimensional model for mesons: G. 't Hooft, Nucl. Phys. B75 461, (1974). Abstract A recently proposed gauge theory for strong interactions, to which the set of planar diagrams play a dominant role, is considered in one space and one time dimension. In this case, the planar diagrams can be reduced to self-energy ladder diagrams, and they can be summed. The gauge filed interactions resemble those of the quantized dual string, and the physical mass spectrum consists of a nearly straight ``Regge trajectory".
Angular constraints and the Melosh transformation: H. Osborn, Nucl.\ Phys. B80, 90 (1974). Abstract The Melosh transformation between current and constituent quarks is discussed when formulated on a light-like plane, as is natural for the description of collinear symmetries like . There is no unique definition of the transformation in this context, but further angular constraints are introduced to ensure that the states coupled by transformations have the correct spin properties. It is then shown that there is no transformation generated by single quark operators which satisfies these requirements, save if only terms to first order in the transverse momentum are kept. Some of the resultant inconsistencies are illustrated by a discussion of baryon magnetic moments. It is concluded that there is no satisfactory explanation of from this approach to the Melosh transformation. A non-field theoretic version of the free quark model which solves these angular constraints is exhibited.
Comment on the null plane gauge: A. Chakrabarti and C. Darzens, Phys. Rev. D9, 2484 (1974). Abstract Gauge invariant Lagrangians are studied using the method of t' Hooft and Veltman with a particular type of noncovariant symmetry breaking term. A limiting case corresponds to the formalism of null plane or light cone quantization. Ward identities and a feature of dimensional regularization are briefly discussed.
Mesons in terms of quarks on a null plane: H. Leutwyler, Nucl.\ Phys. B76, 413 (1974). Abstract The notion of quark wave functions on a null plane is used to give an unambiguous meaning to some of the concepts used in the parton model. We derive sum rules for the meson quark wave functions on the basis of the assumption that the divergences of vector and axial currents are proportional to quark mass terms. Using a simple model for the relation between current and constituent quarks we obtain a set of symmetry relations among the wave functions of the lowest lying U(6) multiplet of mesons. These relations lead to a formula for the non-strange quark mass, MeV. The strange quark mass is constrained to lie between 125 and 150 MeV.
Quarks: currents and constituents: H.J. Melosh, Phys. Rev. D9, 1095 (1974).Abstract An attempt is made to clarify the relation between current quarks and constituent quarks. Assuming that the two are related by a unitary transformation, we outline the properties of this transformation and, in the process, discover a new classification algebra for the hadrons. An example of this transformaton is constructed in the lightlike-plane formulation of the free-quark model, where the transformation is found to be essentially unique and is just the operator solution to the problem of saturating chiral . Using the algebraic structure of the free-quark model phenomenologically, matrix elements of currents between different hadrons are related. This abstraction of free-quark algebraic properties works fairly well for the axial-charge and magnetic-moment operators, although it fails for bilocal operators. Nevertheless, we obtain many successful approximate relations between matrix elements of currents, not the least of which is the recovery of the ratio (proton)/(neutron) = .
Spontaneous symmetry breaking without scalar mesons. II: J.M. Cornwall, Phys. Rev. D 10, 500 (1974). Abstract Recently, the formulation of spontaneously broken gauge theories (SBFT) without scalar mesons was carried out nonperturbatively for Abelian gauge models. These results are reformulated and extended to non-Abelian gauge theories using an effective Lagrangian, which allows symmetry-breaking coefficients to be calculated in perturbation theory. These coefficients appear in Callan-Symanzik equations for the SBGT, which differ only in what is conventionally called the right-hand side from the Callan-Symanzik equations for the symmetric theory. Spontaneous breakdown can only take place if these symmetry-breaking coefficients are positive, in which case the effective Lagrangian reduces, in a certain sense, to the Lagrangian of the symmetric theory. The question of positivity is studied in non-Abelian theories in lowest-order perturbation theory, and it is shown how to accommodate SBGT without scalars in the framework of asymptotic freedom. Some aspects of the utility of the light-cone gauge for calculations in non-Abelian theories are discussed in an appendix.
The Melosh transformation and the Pryce-Tani-Foldy-Wouthuysen transformation: J. S. Bell, Acta Physica Austriaca, Suppl. XIII, 395-445 (1974).
Transformation between current and constituent quarks and transitions between hadrons: F. Gilman, M. Kugler and S. Meshkov, Phys. Rev.\ D9, 715 (1974). Abstract The transformation from current- to constituent-quark basis states is discussed. Certain algebraic properties of the transformed vector and axial-vector currents are abstracted from the free-quark model and assumed to hold in nature. Supplemented by the partially conserved axial-vector current hypothesis and assumptions about the identification of the observed hadrons with simple constituent-quark states, the algebraic properties of the transformed currents are used to compute the pion and photon transitions between any two hadron states. General selection rules are stated. Many specific matrix elements for both meson and baryon decays are tabulated, and both their magnitudes and signs are compared with experiment.
A dual picture for meson resonances in terms of two limiting symmetries: M. Ida, Prog. Theor. Phys. 54, 1775 (1975). Abstract On the basis of lightlike chiral algebra, axial charge couplings of mon resonances are studied in terms of the two limiting symmetries, SU(6)XO(3) and chiral SU(3)XSU(3). By the help of sum rules it is argued that the coexistence of SU(6) and chiral couplings attributes the breaking of one symmetry to the leakage through couplings of the other. Experimental check of this dual picture is made, though it is not conclusive due to the lack of crucial information. The concept of constituent quarks is also discussed in the lightlike formulation.
A lightlike formulation of the quark model: M. Ida, Prog. Theor. Phys. 54, 1519 (1975). Abstract The quark model for hadrons is formulated on the basis of quark fields quantized on a lightlike plane. Hadron resonance states are constructed from the vacuum in terms of creation operators of quarks and antiquarks, where the number of additional pairs are indefinite. Under the non-exoticity assumption for SU(3)XSU(3) irreducible representations, the structure of matrix elements of axial lightlike charge couplings is investigated, and related sum rules of Adler-Weisberger type are obtained. The problem of identifying the quarks on a lightlike plane with charged partons is also discussed.
Chiral symmetry and the quark model: R. Carlitz, D. Heckathorn, J. Kaur, and W.-K. Tung, Phys. Rev. D11, 1234 (1975). Abstract The construction of chiral-symmetric quark models is investigated. We show that the Nambu-Goldstone realization of the chiral symmetry leads naturally to representation mixing of quark states and of their composites. Constructing SU(6) wave functions for hadron states, we obtain a mixing scheme algebraically equivalent to the Melosh transformations. The resulting phenomenology for pionic decays and for weak and electromagnetic vertices is known to be very successful. The present work provides a theoretical basis for these results and opens new avenues for the study of SU(6) symmetry and the investigation of deep-inelastic scattering processes.
Hydrogen atom on null-plane and Melosh transformation: J.S. Bell and H. Ruegg, Nucl. Phys. B93, 12 (1975). Abstract The null-plane dynamics of hydrogen-like atoms is studied in approximations depending on c, the velocity of light, being large. Neglecting terms in the Hamiltonian of order (relative to electron rest energy) a symmetry appears which is analogous to the of hadron classification. This symmetry, if accurate, would dictate zero ground state magnetic moment. The symmetry is broken by terms of third order, which can, however, be transformed away by the appropriate approximation to the Melosh transformation. There then emerges a better symmetry, , broken only at fourth order. The ground state magnetic moment acquires its usual non-relativistic value. The symmetry corresponds to a subgroup of a symmetry which appears in the old Foldy-Wouthuysen approach when spin-orbit coupling is neglected. As well as ``current'' and ``constituent'' pictures, ``classification'' pictures are distinguished; it is to one of the latter that the Melosh transformation transforms.
Positronium on null-plane and Melosh transformation: J.S. Bell and H. Ruegg, Nucl. Phys. B104, 245 (1975). Abstract The null-plane dynamics of positronium-like systems is studied in a quasipotential approach, in approximations depending on c, the velocity of light, being large. Neglecting terms in the quasi-potential of order ( relative to particle rest energy) symmetries appear whose generators are analogous to the good null-plane charges of relativistic hadron classification schemes. These symmetries are broken by terms of order , which can, however, be transformed away by an appropriate approximation to the Melosh transformations. There then emerge better symmetries, broken only at order . When both internal and overall velocities of a composite system are small of first order, and terms of second and higher order are neglected, these better symmetries coincide with those that appear in a Foldy-Wouthuysen description when spin-orbit coupling is neglected. More generally the better symmetries remain good for such a composite system boosted arbitrarily in the three-direction. For this reason we find the original, boost invariant, ``first'' Melosh transformation more appropriate than the ``second'' Melosh transformation.
Quantization of quark fields on a lightlike plane: M. Ida, Prog. Theor. Phys. 54, 1199 (1975). Abstract We investigate some problems in quantizing quark fields on a lightlike hyperplane. The generators of the stability group of the quantization plane and the lightlike charges play a central role. The set of these observables is denoted by . The properties of creation and annihilation operators of quarks are investigated in detail. It is shown that one-particle states can be determined by the measurement of some observables belonging to . Also discussed is the problem of the independent preparation of two-particle states on a lightlike plane.
Quark binding in two dimensions: C. R. Hagen, Nucl. Phys. B95, 477 (1975). Abstract A two-dimensional model recently proposed by 't Hooft to obtain quark binding is considered. It is shown that the model is inconsistent as a result of an anomaly which occurs in the divergence of the current operator. In addition, the claim that the single quark state is suppressed is shown to be the result of an improper treatment of the long range Coulomb interaction.
Spectrum of states in the one-dimensional 't Hooft model: M. S. Marinov, A. M. Perelomov and M. V. Terent'ev, JETP Lett., 20, 225 (1975). Abstract We consider the theory of spinor and vector fields in two-dimensional space time; this theory is invariant with respect to the internal symmetry group SU(N). The interaction is of the Yang-Mills type. The model can be solved in the limit as is the coupling constant). The mass spectrum of the fermion-antifermion system, previously obtained by t' Hooft by summing a certain class of the Feynman diagrams, is obtained.
Confinement, form factors, and deep-inelastic scattering in two-dimensional quantum chromodynamics: M. B. Einhorn, Phys. Rev. D14, 3451, (1976). Abstract We clarify the gauge invariance, infrared structure, and completeness of 't Hooft's solution for the meson sector of two-dimensional quantum chromodynamics. Electromagnetic form factors of mesons are then shown to obey an asymptotic power law, whose power is dynamically determined and is not related to the short-distance behaviour of the theory. Following a review of the total annihilation cross section for producing hadrons, we discuss deep-inelastic lepton scattering. As expected, Bjorken scaling is obtained, but we show how the sum over the hadronic final states reproduces the parton model precisely. The Drell-Yan-West relation and Bloom-Gilman duality are fulfilled for the relation between the scaling function and form factors. We conclude by speculating on the applicability of our picture of form factors to the real four dimensional world. We argue that this is a viable alternative to dimensional scaling and, phenomenologically, the differences between our predictions and the dimensional counting rules are slight for light quarks. Finally, we attempt to abstract those features of the model which may guide us toward a solution to the four-dimensional problem.
Construction of a quark spin operator: R. Carlitz and W.K. Tung, Phys. Rev. D13, 3446 (1976). Abstract We discuss how, in null-plane quantized quark models, the total angular momentum operator can be decomposed into approximately conserved, commuting orbital angular momentum and quark spin operators. This decomposition is relevant for the construction of a (``constituent quark'') classification algebra. Such an algebra has been extensively utilized in phenomenological analyses of matrix elements of the vector and axial-vector currents, but has to date been explicitly constructed only in the free-quark model. Extending this construction to theories of interacting quarks, we identify some features of the free-quark result which are not generally applicable. Specifically, we argue that the algebra is only approximately boost invariant, and that quark pairs provide correction terms in the calculation of current matrix elements.
Gauge fields on a null plane: A. Casher, Phys. Rev. D14, 452, (1976). Abstract The theory of gauge fields interacting with fermions is quantized on the null plane. The singularities of the gauge field propagator are related to the infrared divergences of the theory and cancel in the gauge invariant sector. Ultraviolet divergences are due only to the high transverse momentum behaviour and in the gauge invariant sector are eliminated by coupling constant renormalization. Equivalence to the covariant gauge formulation is proved by explicitly performing the gauge transformation. Gauge invariant ultra violet and infra red cutoffs which preserve unitarity are used wherever necessary. Gauge non-invariant amplitudes are infrared divergent and non-Lorentz invariant.
Light cone quantization: Study of a soluble model with q-number anticommutator: C. R. Hagen and J. H. Yee, Phys. Rev. D13, 2789 (1976). Abstract A massless Dirac field interacting with a massive vector meson in two-dimensional space-time is considered in an attempt to gain further understanding of interacting systems quantized in light-cone coordinates. It is shown that the solution is equivalent not to the same system quantized on a space-like surface, but rather to a single-component fermion model already known in the literature. The commutations relations among the field variables are found to be interaction dependent, with the fermion anticommutator having a q-number term in addition to the usual function. This latter feature may be traced to the fact that the number of degrees of freedom of the light-cone quantized system is fewer than that of the single-component fermion model to which it is equivalent, with this discrepancy in the number of independent dynamical variables being exactly compensated by the interaction-dependent terms in the commutation relations. Some possible applications to four-dimensional space-time are briefly discussed.
Local gauge invariance and the bound-state nature of hadrons: W. Bardeen and R. Pearson, Phys. Rev. D14, 547 (1976). Abstract We analyze those features of non-Abelian color gauge theories which lead to confinement. A consistent picture of hadrons as bound states of quarks and gluons emerges when the vacuum is gauge-invariant. The introduction of a transverse lattice approximation leads to a description of the theory in terms of basic hadronic degrees of freedom and a tractable method for calculation of properties of hadrons.
On the structure of the wave functions of mesons considered as bound states of relativistic quarks: M.V. Terent'ev, Sov. J. Nucl. Phys. 24, 106 (1976). Abstract The restrictions imposed by relativistic invariance on the wave function and the character of the interaction of two bound relativistic particles are studied. The results are applied to the description of mesons as bound states of two light quarks.
Some remarks on null plane quantization: T. Suzuki, S. Tameike and E. Yamada, Prog. Theor. Phys. 55, 922 (1976). Abstract Some features of quantum field theory on a null plane are investigated in comparison with those of conventional formalism on a space-like hyperplane. It is shown that even in a free field theory the light like Hamiltonian should not be introduced in a whole space from the beginning as is usually done. It is also shown that, though the cluster theorem holds good in a sense along the light-like direction, it is impossible to prove Haag's strong convergence asymptotic condition for . In conclusion it seems impossible to construct a consistent scattering theory in the context of quantum field theory on a null plane.
't Hooft bound state equation: A view from two gauges: N. K. Pak and H. C. Tze, Phys. Rev. D14, 3472 (1976). Abstract Two-dimensional U(N)-invariant chromodynamics is canonically quantized in both the light-cone and the axial gauges. A principal value infrared cutoff is adopted. A direct Hamiltonian method leads to two different meson bound state equation in the limit of , kept fixed. In the light cone gauge, 't Hooft's equation is obtained; in the axial gauge, the corresponding equation suffers from covariance problems rooted in the severe infrared divergences of the theory. The Bose form of the model is also presented.
The kinematical structure of lightlike wave functions: M. Ida, Prog. Theor. Phys. 55, 1606 (1976). Abstract Subhadronic wave functions of hadrons in the lightlike quantization are related to the Bethe-Salpeter amplitudes. Their kinematical decomposition is explicitly performed in the lowest sector of any meson. Another method of constructing the wave functions is given by the use of two-component lightlike spinors. The nonrelativistic limit of the wavefunctions is discussed in order to see how the parton picture for hadrons reduce to the conventional quark model picture in the limit of infinite light velocity.
The kinematical structure of lightlike wave functions: M. Ida, Prog. Theor. Phys. 56, 297 (1976). Abstract The kinematical decomposition of subhadronic wave functions of baryons on a lightlike plane is performed in their lowest (qqq) sector. Crucial here is the consideration of the permutation symmetry character of each decomposed part. In a final form of our decomposition there appear only those quantities which are definable on the lightlike plane. The idea of degree expansion is proposed to select important components. The ground baryon octet has only one component of degree zero, which survives in SU(6) limit, and five with degree one.
The problem of mode in the null plane field theory and Dirac's method of quantization: T. Maskawa and K. Yamawaki, Prog. Theor. Phys. 56, 270 (1976). Abstract The null plane quantization is studied with the emphasis on the mode, by using Dirac's quantization for constrained systems. This mode is eliminated from the Hilbert space and the physical vacuum can be obtained in a kinematical way. It enables us to construct the physical Fock space kinematically. Poincare invariance is also studied in detail.
The wave functions in relativistic bound systems: V. Karmanov, Sov.\ Phys. JETP 44, 210 (1976). Abstract Invariant wave functions that appear upon the consideration of a state vector defined on the surface of a light wave front are introduced for the description of bound systems. The main distinction of this parametrization from the nonrelativistic case can be interpreted as a deviation from spherical symmetry at small distances even in the S-wave. A light-cone diagram technique is discussed; the wave functions are related to the vertex functions of this diagram technique. The machinery developed here is necessary for the determination of the high-momentum components of nuclear wave functions, in the relativistic theory of nuclear reactions, and in composite models of elementary particles.
Two-dimensional Yang-Mills theory: A model of quark confinement: C. G. Callan, Jr., N. Coote, and D. J. Gross, Phys. Rev. D13, 1649 (1976). Abstract We analyze the structure of two-dimensional Yang-Mills theory as a model of quark confinement. 't Hooft's solution, in the large N limit, is extended to investigate the consistency and the properties of the model. We construct the hadronic color singlet bound-state scattering amplitudes. We show that they are unitary, that colored states cannot be produced, and that all long range interactions are absent. Current amplitudes are constructed, and we show that the theory is asymptotically and the quark mass sets the scale of mass corrections. The properties of bound states of heavy quarks are discussed, and a dynamical basis for the Okubo-Zweig-Iizuka rule is suggested. We show how confinement can occur with an infrared prescription that leads to finite-mass quarks which decouple from phycical states and discuss the dependence of gauge-variant amplitudes on the cutoff procedure. Higher-order effects in 1/N are shown not to change the qualitative features of the model.
A consistent formulation of the null plane quantum field theory: N. Nakanishi and K. Yamawaki, Nucl. Phys. B122 (1977), Abstract It is shown in the usual framework of quantum field theory that the null plane restriction of a field operator is not a well-defined operator-valued distribution. The cause of the trouble is the so called mode; in order to make it harmless, it is almost inevitable to violate Lorentz invariance. A consistent formulation of the null-plane quantization, which is supposed to be the simplest possible one, is proposed by modifying the definition of Poisson brackets. This theory is invariant under a Poincare subalgebra containing seven generators. It is also shown that the absence of vacuum polarization is realized consistently in this formalism.
Free field theories of spin-mass trajectories and quantum electrodynamics in the null plane: G.R. Bart and S. Fenster, Phys. Rev. D, 3554 (1977). Abstract The ten generators of the Poincaré algebra for quantum electrodynamics and other gauge field theories are given in the null plane such that they are explicitly correspond, in the free-field case, to the Bacry-Chang Group-theoretic forms. The internal oscillator content is extracted for both gauge theories and dual resonance models. In contrast to manifestly covariant or other theories, Bacry-Chang-type generators have the advantages of not referring to dependent spin components and of being rational in the canonical variables. The last property implies a simple position-space representation. Since the forms are independent of spin magnitude and allow inclusion of charge quantum numbers at will, they seem to represent an advantageous free-particle starting point for a hadron field theory with positive spin-mass trajectories (SMT) and with interaction. The interaction terms from manifestly covariant theories are considered in the null plane and found to be cubic and quartic in the fields. A straightforward extension of these interactions to SMT has not been found. The dual model, however, encompasses SMT and is known to have interactions even though the full details of the model's interaction terms are not worked out here. Consequently, the approach indicates how a realistic spectrum might be achieved without composite hadrons and incorporating full Poincaré invariance.
Null plane field theory: J. S. Bell and H. Ruegg in Quarks and Hadronic Structure: Proceedings of the international workshop of the Ettore Majorana Center for scientific culture, Erice, Italy, September 1975, edited by G. Morpurgo, Plenum Press, New York (1977). Abstract A sketch is given of an approach to null plane field theory which (it is hoped) illuminates the relation between the relativistic parton model, the non-relativistic quark model, and various SU(6) and SU(6) broken symmetry schemes, including those of Melosh.
Physical particles of the massive Schwinger model: H. Bergknoff, Nucl. Phys. B122, 215 (1977). Abstract The massive Schwinger model is considered in the infinite momentum frame. By assuming its physical particles consists of two fermion bound states, we compute a spectrum. For fermions with large bare masses, the method is reliable. For low mass fermions, we find we must include states of higher fermion number to adequately describe excited states of the fundamental boson of the theory. We do this for the scalar state in the limit of small bare fermion mass. This represenation of the theory provides a unified treatment of both the weak and strong coupling limits, remaining in the fermion representation throughout. We have checked our numerical results with the exact calculations wherever possible, and find good agreement.
Surface medication for gauge theories in two dimensions: M.B. Halpern and P. Senjanovic, Phys. Rev. D15, 3629 (1977). Abstract When surface terms cannot be neglected, the usual canonical formalism is plagued by a host of ambiguities and inconsistencies. We review these problems in the context of the massive Schwinger model, and present a complete cure effected by a well-chosen dynamical surface term. In the presence of the surface term, the canonical formulation can again be naive. We also offer an introductory application of the method to the non-Abelian case: In a box, only singlet states are possible. The ``new'' singlet states involve surface excitation and may not survive the large-box limit.
Two-dimensional SU(N) gauge theory, strings and wings: Comparitive analysis of meson spectra and covariance: A. J. Hanson, R. D. Peccei and M. K. Prasad, Nucl. Phys. B121, 477 (1977). Abstract 't Hooft's two-dimensional SU(N) gauge theory model for mesons is studied in two different axial gauges. Using numerical techniques employed in aerodynamical wing theory, we compare the bound state spectra in the gauge and gauges, finding agreement in the weak coupling limit. Furthermore, Lorentz covariance of the weak coupling theory is numerically confirmed. We also investigate the massive-end string model, which is equivalent to 't Hooft's model when the gauge is chosen. We find that the numerical spectrum of the string model in the gauge differs from the gauge string spectrum as well as from the gauge theory spectrum. A Bethe-Salpeter equation approach to the spectrum of the gauge theory in the gauge is developed for any coupling. While the strong coupling theory in this gauge presents severe difficulties, the weak coupling limit is shown to be completely consistent.
Covariant two body dynamics and the Weinberg equation: J. M. Namyslowski, Phys. Rev. D18, 3676 (1978) . Abstract Covariant, constraint two body dynamics with both particles put on their mass shells, is proposed as a generalization of the Bakamjian-Thomas-Coester relativistic quantum mechanical scheme. The Weinberg infinite momentum limit of the latter scheme is investigated, and a covariant formulation of the two body problem in the light front field theory approach is made. We find several equivalent versions of the three dimensional covariant two body integral equations. Among these equations we get one in which the covariant two body propagator has the form identical with the nonrelativistic case, i.e., we have a quadratic structure in the relative momentum and the ordinary reduced mass. We discuss connections between various schemes, emphasizing the variety and the uniqueness of the off-shell extensions.
Expression for relativistic amplitudes in terms of wave functions: V. Karmanov, Sov. Phys. JETP 48(4), 598 (1978). Abstract The conditions under which relativistic amplitudes can be expressed in terms of wave functions are investigated within the framework of an invariant diagram technique that appears in a field-theoretical treatment of a light front. The obtained amplitudes depend on a 4-vector that defines the surface of the wave front. A prescription is formulated for the determination of values of the 4-vector that minimize the diagram contribution which is not expressed in terms of the wave functions. This investigation is the equivalent of a study of the dependence of the amplitudes of the old perturbation theory in a system with infinite momentum on the direction of the infinite momentum.
Relativistic dynamics on a null plane: H. Lewtwyler and J. Stern, Ann. Phys. 112, 94 (1978). Abstract In view of the possible application to the quark model and hadron spectroscopy, we investigate relativistic hamiltonian quantum theories of finitely many degrees of freedom. We make use of the fact that if the null planes are used as initial surfaces, the strucure of the theory closely resembles nonrelativistic quantum mechanics: the inner variable that describe the structure of the system uncouple from the motion of the system as a whole. The dynamical content of such a theory resides in the operators M, J of mass and the spin that act in the space carrying the inner degrees of freedom. Relativistic invariance is equivalent to the requirement that M and J generate a unitary representation of U(2). In contrast to this requirement, the condition that the wave function of the system transform covariantly strongly restricts the dynamics. It is proven that for systems containing two constituents, covariance is equivalent to an algebraic relation that involves M and J - the angular condition. A class of solutions of the angular conditions is provided by a particular type of manifestly covariant wave equation. One nontrivial solution of this class, a relativistic oscillator is given in detail. Confinement models of this type represents an interesting alternative to the solutions of the angular condition that result from the perturbation expansion of a local field theory through the three dimensional quasi potential version of the Bethe-Salpeter equation.
Asymptotic freedom in the infinite momentum frame : C. B. Thorn, Phys. Rev. D20, 1934 (1979). Abstract We study the renormalization of SU(N) Yang-Mills theory through one-loop in the null plane gauge. We choose as a measure of the effective coupling the off shell four gluon correlation function with all legs having zero transverse momentum. We find that in addition to self energy and vertex correction, two gluon exchange contributes to coupling constant renormalization in an essential way. In this gauge asymptotic freedom is due to a residual attraction between two gluons in the ultra violet domain.
Fock space description of the expansion of QCD: C. B. Thorn, Phys. Rev.D20, 1435 (1979) . Abstract We present a Fock space formulation of the expansion of QCD in a power series in , where is the number of colors. We hope this formulation will aid spectrum calculation in the limit.
On the formulation of two- and three-body relativistic equations employing light-front dynamics: B.L.G. Bakker, L.A. Kondratyuk and M.V. Terent'ev, Nucl. Phys. B158, 497-519, (1979). Abstract Using the light-front hamiltonian with two-body forces depending on internal variables only, we derive relativistic three-dimensional equations for the two- and three-body scattering operators.
Quantum kinks on the null plane: J. Baacke, Z. Physik C, Particles and Fields 1, 349 (1979). Abstract We consider the quantization of a 1+1 dimensional field theory with kink solutions on a null plane. We present a field expansion which diagonalizes the operator including first order quantum corrections, reobtaining thereby the well known result for the kink mass. The quantization scheme treats classical solutions of different rapidity on an equal footing and the translation mode cancels completely, at least in the order considered here.
Quark confinement in the infinite momentum frame: C. B. Thorn, Phys. Rev. D19, 639 (1979) . Abstract We formulate the problem of quark confinement in the infinite momentum frame. In this frame the dynamics is naturally described as a many body problem: Quarks and gluons can be thought of as nonrelativistic particles moving in the two dimensional transverse space with mechanical mass related to the longitudinal momentum . In this language a natural quark confining mechanism is the condensation of gluons along a tube joining a seperated quark and an anti quark. This condensation is favoured by two circumstances: 1) the fact that the bare gluons are massless reduces the minimum energy for gluon pair production to zero, and 2) the octet color structure allows gluons to form into chains with long range attractive nearest neighbour interactions. We investigate the viability of this mechanism first in the limit fixed, where is the number of colors in the theory. We analyze in detail a simplified version of the dynamics which preserves the essential features of the full problem. This simplified model exhibits quark confinement and describe mesons as relativistic open strings. It also yields a relationship between the Regge slope and the scale measured in deep inelastic leptoproduction: , which is not too far from the experimental number . We discuss next, the problem of finite . We argue that the expansion is likely to have a vacuum instability which must be handled nonperturbatively before corrections could be calculated. We suggest that the true vacuum is a condensate of closed strings which have a finite density by virtue of repulsive interactions inherent in the 4-gluon term in the Hamiltonian. A crude estimate of the condensate energy density yields an order of magnitude estimate relation of the form should be a rough estimate of the thickness of the string.
Relativistic repulsive effects in nonrelativistic systems: P. Danielewicz and J. M. Namyslowski, Phys. Lett. 81 B, 110, (1979). Abstract A ladder approximation to the Weinberg equation constitutes a basis for a study of relativistic effects in a model two-nucleon system. The essential changes in the low energy phase shifts and in the ground state are recovered when passing from a nonrelativistic to the relativistic treatment. Signs of the relativistic corrections are such as if the interaction were becoming more repulsive.
Exclusive processes in perturbative quantum chromodynamics: G. P. Lepage and S. J. Brodsky, Phys. Rev. D22, 2157 (1980). Abstract We present a systematic analysis in perturbative QCD of large momentum transfer exclusive processes. Predictions are given for the scaling behaviour, angular dependence, helicity structure, and normalization of elastic and inelastic form factors and large angle exclusive scattering amplitudes for hadrons and photons. We prove that these reactions are dominated by quark and gluon sub processes at short distances and thus that the dimensional counting rules for the power law fall off of these amplitudes with momentum transfer are rigourous predictions of QCD, modulo calculable corrections from the behaviour of the hadronic wave functions at short distances. These anomalous dimension corrections are determined by evolution equations for process independent meson and baryon ``distribution amplitudes" , which controls the valence quark distributions in high momentum transfer exclusive reactions. The analysis can be carried out systematically in powers of , the QCD running coupling constant. Although the calculations are most conveniently carried out using light cone perturbation theory and the light cone gauge, we also present a gauge independent analysis and relate the distribution amplitude to a gauge invariant Bethe-Salpeter amplitude.
Hadron masses in quantum chromodynamics on the transverse lattice: W.A. Bardeen, R.B. Pearson, and E. Rabinovici, Phys. Rev. D, 1037 (1980). Abstract Calculational methods are formulated for the transverse lattice version of quantum chromodynamics. These methods are used to study the low-lying spectrum of gluon bound states in the pure Yang-Mills theory.
Light front wave function of a relativistic composite system in an explicitly solvable model: V. A. Karmanov, Nucl. Phys. B166, 378 (1980). Abstract The light front wave function of a composite system, consisting of two scalar particles interacting by means of massless scalar particle exchange (Wick-Cutkosky model) is calculated. The wave function obtained coincides with that in the Coulomb potential at nonrelativistic particle momentum, but due to retardation of interaction, depends also on an additional variable having the form of a unit vector. It is emphasized that for the correct parametrization of the nuclear and hadronic wave functions at relativistic relative momenta, it is necessary to take into account their dependence on this additional variable.
Noninstantaneous O(v/c) relativistic effects in bound states and a covariant Schrodinger equation: P. M. Fishbane and J. M. Namyslowski, Phys. Rev. D21, 2406 (1980). Abstract The noninstantaneous and nonlocal interactions which follow from Weinberg type dynamics are found to produce v/c relativistic corrections to potentials which are nonrelativistic limits of certain field theoretic dynamics. Such corrections may be applicable in for example phenomenological models of charmonium. These interactions are driving terms in a covariant three dimensional two body integral equation derivable from field theory. For bound systems this equation is a fully covariant Schrodinger equation, with space like relative momentum and a proper angular resolution. We study this equation, including its systematic relativistic corrections, in various limits based on scalar-particle-exchange dynamics. We compare and contrast it to a related but different three-dimensional equation derivable from field theory which represents an equal-time projection. We also comment on other approaches to the relation between relativistic and nonrelativistic dynamics.
Problems of Quantization in the infinite momentum frame: P. J. Steinhardt, Ann. Phys. 128, 425 (1980). Abstract Various problems of quantization in the infinite momentum frame are discussed. Naive application of the Dirac procedure is shown to yield inconsistent results. A rigrous method of proceeding from an action to a Hamiltonian with consistent equal-time commutators is proposed. The method is applied to a free, massive scalar field theory, the non-linear sigma model in 1+1 dimensions and quantum electrodynamics in 3+1 dimensions.
The scattering problem for relativistic systems with a fixed number of particles in light-front dynamics: L.A. Kondratyuk and M.V. Terent'ev, Sov.\ J. Nucl. Phys. 31(4), 561 (1980). Abstract The scattering problem is formulated for a system with a fixed number of particles in light-front dynamics, which is treated as the infinite-momentum limit of instant-form dynamics. The properties of spin states are studied. A technique is developed for constructing a partial-wave expansion of the scattering amplitudes in light-front dynamics. The form which the phenomenological potentials may take in the question for the scattering matrix is discussed. These potentials must be consistent with relativistic invariance. Equations are derived for the scattering matrix in relativistic systems of two and three particles.
Exclusive processes and hadron dynamics at short distances: S. Brodsky and G. Lepage, Phys. Scripta 23, 945 (1981). Abstract The predictions of perturbative QCD for a number of areas of hadron dynamics are discussed, including exclusive processes at large momentum transfer, the endpoint behavior of hadronic structure functions, and the Fock state structure of hadron wavefunctions - especially their behavior at short-distance. New results for exclusive two-photon processes, the normalization of higher twist contributions to the meson structure function, and the calculation of the valence Fock state probability of the pion are presented. We also review the contrasting features of QCD and parton model dynamics.
High energy phenomena, short range nuclear structure and QCD: L.L. Frankfurt and M.I. Strikman, Phys. Rep. 76, 215 (1981). Abstract A systematic review and theoretical analysis of the experimental data on multi GeV lepton, photon, hadron, deuteron(nucleus) reactions from nuclei forbidden in the scattering from free nucleons is discussed. It is shown that all these data can be quantitatively described as a manifestation of short range few nucleon correlation. Calculations for elastic and deep inelastic electromagnetic and weak form factors of the deuteron and other nuclei are given. The inclusive production of leading particles in the nucleus fragmentation region in high energy lepton, hadron or nuclear induced collisions is analyzed. The straightforward correspondence between the Weinberg equation for the light cone wave functions of the deuteron and the nonrelativistic equation is found. It is shown that the predictions of QCD for short distance phenomena in nuclei are in agreement with both the experimental data and theoretical expectations due to short distance correlations in nuclei. Several feasible experiments are considered which could establish the existence of relativistic nuclear physics.
On the light cone formulation of classical non-abelian gauge theory: V.A. Franke, Y.V. Novozhilov and E.V. Prokhvatilov, Lett. Math. Phys. 5, 239 (1981). Abstract For a classical Yang-Mills field which is periodic in the longitudinal light cone coordinate a) a gauge condition is formulated b) presence of field singularities in this gauge is shown and c) the relevance of these singularities to the topological charge is demonstrated.
On the light cone quantization of non-abelian gauge theory: V.A. Franke, Y. V. Novozhilov and E.V. Prokhvatilov, Lett. Math. Phys. 5, 437 (1981). Abstract The implications of periodic boundary conditions in the light cone quantization of non-abelian fields are studied. Formulation of the theory in the singularity-free case is presented. Some consequence of field singularities are discussed.
Relativistic deuteron wave function on the light front: V. Karmanov, Nucl. Phys. A362, 331 (1981). Abstract In the framework of the one-boson-exchange model the approximate analytical expression for the deuteron wave function (WF) at relativistic relative momenta is obtained. The WF depends on the extra variable having the form of a unit vector and is determined by six functions instead of two (S- and D-waves) for the non-relativistic case. At moderate momenta the WF is matched with the WF in the Reid model. The importance of indicating the qualitative observed phenomena associated with the change of parametrization and spin structure of the relativistic deuteron WF in comparison with the non-relativistic one is emphasized.
Dirac's light-cone coordinate system: Y.S. Kim and M.E. Noz, Am. J. Phys. 50(8), 721 (1982). Abstract It is shown that Dirac's light-cone coordinate system provides an effective method for treating the geometry of Lorentz transformation in a rectangular coordinate system. Transformation properties of the coordinate variables and those of the derivatives are discussed in detail. The Lorentz boost along a given direction is shown to be a coordinate transformation in which ``cross products'' are preserved. It is pointed out that the Lorentz boost is a symplectic transformation.
Deuteron structure in the elastic electron-deuteron scattering: St. Glazek, Acta. Phys. Pol. B14, 893 (1983). Abstract The relativistic light front dynamics, which unifies the descriptions of low and high energy phenomena, is applied to the deuteron. The deuteron wave function is constructed from the Weinberg equation with spin, under the constraints of the quark substructure of the deuteron current. It is shown that the relativistic nucleon impulse approximation of deuteron is insufficient to explain the experimental data for the elastic electron- deuteron scattering at momentum transfers of the order of 8 GeV.
Hadronic wavefunctions in QCD: G. Peter Lepage, S. J. Brodsky, T. Huang, and P. B. Mackenzie, in Particles and Fields 2, edited by A. Z. Capri and A. N. Kamal (Plenum, New York, 1983)
Light-cone superspace and the ultraviolet finiteness of the N=4 model: S. Mandelstam, Nucl. Phys. B213, 149 (1983). Abstract Sueprspace in the light-cone frame takes a simple form. No auxiliary fields are necessary, and application to extended supersymmetries is straightforward. It is shown that the N=4 model, in a certain form of the light-cone gauge, is completely free of ultraviolet divergences in any order of perturbation theory. It follows that the -function vanishes in any gauge, to all orders of perturbation theory. Our method differs from the conventional method in that we use only half the number of 's as there are supersymmetry operators. All fields are unconstrained and independent of the 's.
Manifestation in the reaction of relativistic effects in the deuteron: V.A. Karmanov, Pis'ma Zh. Eksp. Teor. Fiz. 38, 311 (1983). Abstract The description of the deuteron by means of a relativistic wave function at the light front increases the theoretical value of for the reaction in the region 1/2;SPMlt;x;SPMlt;1 and eliminates the existing discrepancy with experiment [P. Bosted et al., Phys.\ Rev. Lett. 49 1380 (1982)]. At 0;SPMlt;x;SPMlt;1/2, on the other hand, the cross section is predicted to decrease. These two qualitative effects are manifestations of one extremely common property of a nonsimultaneous wave function.
Relativistic two-nucleon calculations on the light front: L. Müller, Il Nuovo Cimento 75A, 39 (1983). Abstract The relativistic theory for few-nucleon systems developed by Glöckle and Müller is transformed into the light front formalism. For a model of scalar particles exchanging scalar mesons the 10 generators of the Poincaré group are derived in pure particle space up to lowest order in the coupling. Because of the impossibility of a complete partial-wave decomposition on the light front, only bound states can be calculated numerically. This is done for the two-body system. The results differ from those at an instant because of the omission of higher-order terms.
Generalized Ward identities for the quark self energy and the quark-quark-gluon vertex in the light cone gauge: G. Leibbrandt and S.-L. Nyeo, Phys. Lett. 140B, 417 (1984). Abstract A light cone gauge formalism, developed recently by one of the authors, is applied to the one-loop quark self-energy and the quark-quark-gluon vertex function which are shown to respect the generalized Ward identity. The possible renormalization in this prescription is briefly discussed.
Generalized Ward identity for the quark self-energy and the quark-quark-gluon vertex in the light-cone gauge: G. Leibbrandt and S.L. Nyeo, Phys. Lett. 140B, 417 (1984). Abstract A light-cone gauge formalism, developed recently by one of the authors, is applied to the one-loop quark self-energy and quark-quark-gluon vertex function which are shown to respect the generalized Ward identity. The possible renormalization in this prescription is briefly discussed.
Hadron-hadron collisions at extreme energies: Light cone QCD with an axial vector anomaly current and an infra red fixed point: A. R. White, Phys. Rev. D 29, 1435 (1984) . Abstract We argue that QCD with maximum number of fermions allowed by asymptotic freedom provides a ``parton model" description of soft high energy collisions. That is, infinite momentum quantization can be based on the perturbative vacuum and yet produce confinement and chiral symmetry breaking. A first-stage infra-red construction gives SU(2) gauge invariance and confinement. An infrared fixed point produces transverse momentum scaling and associated infrared divergences which couple to an anomaly current component of a Fock space wave function. The divergence factor onto color zero states needed by transverse gauge invariance. Parton interactions are dominated by fermion loop anamolies coupled to the divergences. As a result a pion has a vector valence quark component. The infrared limit giving SU(3) gauge invariance is argued to be accompanied by critical Pomeron high energy behaviour and spontaneous chiral symetry breaking, but is only briefly discussed in this paper.
Light-cone gauge in Yang-Mills theory: G. Leibbrandt, Phys. Rev. D, 1699 (1984). Abstract A prescription for massless Feynman integrals in the light-cone gauge , , is suggested which leads to well-defined and exact, but Lorentz-noninvariant, integrals. As a result the Yang-Mills self-energy is likewise Lorentz noninvariant, but remains transverse in agreement with the Ward and Becchi-Rouet-Stora (BRS) identities. It is also shown that the assumption of Lorentz invariance of the integrals, coupled with the validity of the Ward (BRS) identity, leads to a nonlocal Yang-Mills self-energy.
Light front solution to problems of conventional approach to deep inelastic electron-deuteron scattering: St. Glazek, Acta Phys. Polon. B18, 85 (1984). Abstract We present a model light front calculation of the inelastic electron-deuteron scattering within the conventional two nucleon approximation. The results lead to the clear interpretation of the convolution formula expressing structure functions of the deuteron by structure function of nucleons. Several ambiguities of this formula, including the West correction and the Bodek ambiguity, are resolved. We use a simple quark model for the nucleon structure, guided by the counting rules. In extracting the neutron structure from th deuteron and the proton data we find that the dynamical off-shell effects in the nucleon structure functions are larger than the properly calculated smearing corrections.
On the evaluation of integrals in the light-cone gauge: D.M. Capper, J.J. Dulwich, and M.J. Litvak, Nucl. Phys. B241, 463 (1984). Abstract We consider the evaluation of Feynman integrals in the light-cone gauge. The various prescriptions that can be used to remove the ambiguities arising in this gauge are discussed. As an example we evaluate the one-loop contribution to the gluon self-energy in N = 4 supersymmetry. Only the gluon loop contribution differs from the usual covariant result and this can be shown to involve only one integral peculiar to the light-cone gauge. Dimensional regularization is employed to evaluate this integral using both the principal value prescription and the prescription suggested by Mandelstam.
Relativistic effects in the deuteron binding energy: St. Glazek, Acta Phys. Polon., B15, 889 (1984). Abstract The binding energy of a two nucleon system is calculated from the relativistic Weinberg equation with spin, and from its nonrelativistic limit. We get that the interaction of nucleons inside the deuteron is largely different from that of nonrelativistic particles, in spite of the fact that the binding energy is very small. The relativistic interaction is less attractive than the nonrelativistic one. An inclusion of spin introduces significant dynamical effects. The light front dynamics, used in our calculations, has unique advantage over other existing approaches. The practical values of this sheme, including the invariant spinor representation are presented in full detail.
Three-quark interaction: The driving force in the inhomogeneous evolution equations: E. A. Bartnik and J. M. Namyslowski, Phys. Rev. D30, 1064 (1984). Abstract Using perturbative QCD on the light cone ( A=0 gauge), and the Brodsky-Lepage collinear projection, we make a partial wave projection (in the component) of the Weinberg equation , and find a set of evolution equations for distribution amplitudes. For 0 our equations are inhomogeneous and their solutions show an increasing QCD perturbative effect for the currently available momentun transfers. The driving force of the inhomogeneous evolution equations is a three quark irreducible interaction, which gives terms in the proton's deep inelastic structure function, breaks the SU(6) symmetry, and contributes to the derivation of the (d/u) ratio for proton from the value (1/2). The force couples a pair to one transverse gluon and one Coulomb term.
Constructing mesons in the infinite momentum frame: R. Brout and J.F. Lagae, Nucl. Phys. B255, 609-616 (1985). Abstract It is shown that the study of light quarks in a confining potential is simplified by using the infinite momentum frame, in particular for obtaining the pion. For massless quarks in two-dimensional space-time 't Hooft's zero-mass bound state is a consequence of the cancellation between the positive energy contained in the flux tube and the negative (exchange) self-energy of the quarks. In four dimensions, the value of the self-energy is doubled but there is transverse kinetic energy as well. If one identifies the ground state with the pion, hence of zero mass, the condition of cancellation gives a value for the radius of the pion in terms of the confinement length scale.
Discretized light cone quantization: Solution to a field theory in one space and one time dimension: H. C. Pauli, and S. J. Brodsky, Phys. Rev. D32, 2001 (1985). Abstract In the preceding paper, the field-theoretic bound state problem in 1+1 dimensions was mapped to the problem of diagonalizing a strictly finite dimensional Hamiltonian matrix by quantizing at equal light cone time. In this paper, we calculate the invariant mass spectrum for the Yukawa theory . The spectrum is shown to be independent of the momentum cut off in the limit and more complex with increasing harmonic resolution K. The results are compared with the recent works of Brooks and Frautschi, who apply conventional space-time quantization. Because of incompatible cutoffs, we reproduce their results only qualitatively, for a rather small value . We propose an explanation for their nonunique mass renormalization. We also discuss the straightforward application of the discretized light cone quantization to non-Abelian field theories in 1+1 dimensions, and the generalization to 3+1 dimensions.
Evolution equation and relativistic bound state wavefunctions for scalar field models in four and six dimensions: S.J. Brodsky, C.R. Ji and M. Sawicki, Phys. Rev. D32, 1530 (1985). Abstract We investigate the evolution equation for distribution amplitudes in the framework of a scalar theory quantized on the light cone. We find general solutions for the cases of 4 and 6 dimensions and use them to reconstruct two body relativistic bound state wave functions at small distances. The relation between light cone bound state equation and the Bethe-Salpeter equation is discussed.
General calculation of the supersymmetric Yang-Mills self-energy in an effective light-cone gauge formalism: G. Leibbrandt and T. Matsuki, Phys. Rev. D31, 934 (1985). Abstract The N=4 supersymmetric Yang-Mills self-energy is calculated, to one-loop order, in a light-cone gauge that respects power counting and locality of the integrals. The calculation is general, including both physical and unphysical modes (fields). It is found that the self-energy satisfies the Ward identity and that it is infrared finite, but ultraviolet divergent.
Light cone perturbation theory and its application to different fields: J. M. Namyslowski, Progress in particle and nuclear physics, Vol. 14, edited by A. Faessler, Pergamon Press (1985). Abstract The field theoretical foundations of the light cone perturbation theory including QCD are reviewed on the basis of the original papers. Great attention is paid to the systematic account of the spin effects in the light cone scheme. We also emphasize the role of the Jacobi relative momenta in giving an invariant formulation of the light cone approach and proving the cluster decomposition property. These features are very important in the relativistic dynamics of many body systems. There is stressed the existence of the physical vacuum in the light cone approach, which allows to build the Fock space basis. This gives the possibility of formulating systematic approximations to the structure of hadrons. There are given examples of sizable relativistic repulsive effects and there is stressed the presence of a 3 quark irreducible force, which plays an essential role in the deep inelastic structure of nucleon and other nuclei. We show the asymptotic behaviour of the elastic electromagnetic form factors of bound states and indicate that to account for the deuteron experimental data it is insufficient to treat only the mesonic and nucleonic degrees of freedom ( one must go to the quark level ).
Slow and fast quarks in nucleons: A. G azek, S. G azek, E. Werner, and J.M. Namys owski, Phys. Letts. 158B, 150 (1985). Abstract Using light-front dynamics, and the notion of the running effective quark mass, we propose a model of the three-quark nucleon wave function, which accounts simultaneously both for the low and the high energy experimental data. Our wave function is a product of a spinor part, inferred from the QCD sum rules, and a gaussian scalar factor, taken for simplicity. Including all three Ioffe currents we get from one wave function both the negative neutron charge radius fm and the decreasing d/u ratio in the proton for increasing from 0.5 to 1.
Solution of the light cone equation for the relativistic bound state: M. Sawicki, Phys. Rev. D32, 2666 (1985). Abstract The ladder approximation to the bound state equation at equal light cone time is investigated in the framework of scalar theory. With the help of Fock transformation the equation is reduced to an eigen value problem for a compact operator. The eigen solution for the ground state is found.
Solving field theory in one space and one time dimensions: H. C. Pauli, and S. J. Brodsky, Phys. Rev. D32, 1993 (1985). Abstract By quantizing a realistic field theory in one space and one time dimension at equal light cone time rather than at equal time t, one can find exact solutions to the bound state problem. The method is nonperturbative and amounts to the diagonalization of finite matrices in Fock space. It applies also for non-Abelian gauge theory in 1+1 dimensions, but is demonstrated here for the simple case of fermions interacting with scalar fields. The success of the light cone quantization method rests on the existence of a new dynamical quantum number, the harmonic resolution K, which can be understood as the ratio of a characteristic length, the box size L, and the Compton wavelength of a massive particle. We emphasize the appearance of self-induced instantaneous inertias.
The effective potential in the light-cone gauge and supersymmetric Yang-Mills theories: D. Capper and D. Jones, Nucl. Phys. B252, 718 (1985). Abstract We evaluate the one-loop effective potential, , in the light-cone gauge for a general gauge theory with arbitrary scalar and fermion representations. In the case of a general N=1 supersymmetric gauge theory the result for is simpler than in the Landau gauge: the form of STr is particularly elegant, and in one-loop finite theories we find STr. We show how the renormalisation group relates STR to the scalar anomalous dimension, , and we give an explicit calculation of in the light-cone gauge.
The light-cone gauge and the principal value prescription - Ward identities in Yang-Mills theories: H.C. Lee and M.S. Milgram, Z. Phys. C - Particles and Fields 28, 579 (1985). Abstract By explicit calculation of radiative corrections to the self-energy and the three-vertex at one-loop level for Yang-Mills theories in the light-cone gauge, it is demonstrated that analytically regulated Feynman integrals defined by the principal value prescription satisfy the one, two, and three-point Ward identities. However, both the calculated self-energy and three-vertex have anomalous, unrenormalizable infinite parts, thus confirming the belief, based on previous calculations of only the self-energy, that the principal value prescription is seriously flawed in the light-cone gauge.
The light-cone gauge at two loops: the scalar anomalous dimension: D. Capper, D. Jones and A. Suzuki, Z. Phys. C - Particles and Fields 29, 585 (1985). Abstract We demonstrate that the light-cone gauge is a feasible tool for multi-loop computations by using it to evaluate the two-loop scalar anomalous dimension, , in a general gauge theory. In the special case of supersymmetry we obtain agreement with previous results which were derived using nonlight-cone techniques.
Yang-Mills theories in the light-cone gauge: A. Bassetto, M. Dalbosco, I. Lazzizzera, and R. Soldati, Phys. Rev. D31, 2012 (1985). Abstract We develop the Hamiltonian quantization of Yang-Mills theories in the light-cone gauge, obtaining the well-defined prescription for the gluon propagator, previously proposed in the literature. A Hilbert space with indefinite metric emerges in which the role of the residual gauge freedom is clarified. It is possible to define consistently a subspace with positive-semidefinite inner product where Gauss's law and Poincaré covariance are recovered and the perturbative S matrix is unitary.
Analytical calculation of the bound state spectrum in the light cone two-body equation: C.R. Ji, Phys. Lett. 167B, 16 (1986). Abstract Relativistic bound states are analyzed with the light cone formalism of the Bethe-Salpeter equation in the Wick Cutkosky model. A simple analytic relation between the couping constant and the binding energy is derived for all the nl states and the Balmer formula is recovered in the nonrelativistic limit. A valid analytic solution of the light cone two body equation is presented.
Bound state spectrum from the light cone two-body equation in theories: C.R. Ji and R.J. Furnstahl, Phys. Lett. 167B, 11 (1986). Abstract The relativistic bound state problem with the light cone two body equation (i.e., the Bethe-Salpeter equation in the infinite momentum frame) is investigated in the light cone ladder approximation to theories. A variational principle is found for the eigenvalues. Numerical results are compared with some existing calculations and with some new analytic results.
Eigensolutions of the light-cone equation for a scalar field model: M. Sawicki, Phys. Rev. D33, 1103, (1986). Abstract The ladder approximation to the bound-state equation at equal light-cone time is investigated in the framework of a scalar field theory. With the help of the Fock trandformation the equation is reduced to an eigenvalue problem for a compact operator. Eigensolutions for lowest-energy levels are found and compared with results of the covariant ladder approximation. In the positronium region both schemes yield equivalent eigenvalues, in agreement with predictions of perturbation theory. For strongly bound systems, however, both schemes give different results. The eigenfunctions are explicitly given and their asymptotic behaviour is analyzed.
Nonlocal BRS counterterms in a physical gauge: G. Leibbrandt and S. Nyeo, Nucl. Phys. B276, 459 (1986). Abstract The general three-gluon is calculated to one-loop order in the physical light-cone gauge , . It is shown that a

modified BRS ansatz for the counterterms satisfies not only the gluon self-energy , but also the local and nonlocal terms in . It is found that the number of local counterterms is finite.
The triangle anomaly in the light-cone gauge: D. Capper, D. Jones and M. Litvak, Z. Phys. C - Particles and Fields 32, 221 (1986). Abstract It is shown that the triangle anomaly can be evaluated in the light-cone gauge and that the result obtained is consistent with the usual covariant one. We use two different procedures: (i) Eliminating the non-physical fields from the covariant anomalous Ward identity. (ii) Carrying out a chiral transformation on the light-cone Lagrangian. The use of both dimensional and Pauli-Villars regularisations are discussed.
Three body force in the three nucleon system, eds. B.L. Berman and B.F. Gibson, Lecture Notes in Physics, Vol. 260, Spring-Verlag, Berlin (1986).
Two Yang-Mills theories in the light-cone gauge: complete one-loop counterterm: H. Lee and M. Milgram, Nucl. Phys. B268, 543 (1986). Abstract The Mandelstam-Leibbrandt prescription is used to study the one loop structures of the two-component (LCM2) and four-component (LCM4) formalisms of the same Yang-Mills theory in the light-cone gauge. The complete one-loop counter lagrangians are constructed by computing the one-loop two-, three- and four-point vertices. LCM2 is renormalizable order-by-order in g with , . For LCM4, both the two- and three-vertices generate anomalous counterterms which, however, cancel upon summation so that the total is the same as LCM2. Slavnov-Taylor identities are satisfied in LCM4; they do not exist in LCM2. The method of analytic regularization is used in computation; all invariant and tensor integrals are evaluated using a single representation for light-cone invariant two-point integrals. The calculation is exceedingly simple in LCM2, far less so in LCM4.
Covariant light front perturbation theory and three-particle equations: M.G. Fuda, Phys. Rev. C35, 226 (1987). Abstract A covariant version of light front perturbation theory is obtained as a limit of the covariant time-ordered perturbation theory developed recently by the author. The graphical rules for the covariant light front perturbation theory are essentially the same as Weinberg's infinite momentum frame rules; however, they involve a redefinition of the original Weinberg variables. The new definitions guarantee that the contributions of individual diagrams to the S matrix are invariant. A set of manifestly invariant three-particle integral equations is derived. These equations are obtained from a model field theory which describes the interaction of a charged scalar particle with a neutral scalar particle according to the virtual process . The solutions of the integral equations lead to amplitudes for and which satisfy two- and three-particle unitarity. The integral equations are free of the spurious singularity in s, the square of the invariant c.m. energy, which has been an undesirable feature of earlier relativistic three-particle equations. This singularity is known to be responsible for spurious bound state solutions.
Discretized light cone quantization: The massless and massive Schwinger model: T. Eller, H. C. Pauli, and S. J. Brodsky, Phys. Rev. D35, 1493 (1987). Abstract The method of Discretized Light Cone Quantization (DLCQ), recently proposed for obtaining non-perturbative solutions to field theories, is applied to quantum-electrodynamics in one space dimension (QED). The spectrum of invariant masses and the eigenfunctions of the light-cone Hamiltonian are calculated; i.e., the bound state problem is solved for all values of the coupling constant. For very strong coupling (Schwinger model proper) DLCQ reproduces one-to-one the known exact solutions. For nonvanishing fermion mass (massive Schwinger model) the results of DLCQ agree with earlier work and in particular with a lattice gauge calculation.
Introduction to noncovariant gauges: G. Leibbrandt, Rev. Mod. Phys. 59, 1067 (1987). Abstract The most important single attribute of noncovariant gauge is their ghost free nature. Although noncovariant gauges have been an integral part of quantum field theory for many decades, their effectiveness in the quantization of non-Abelian theories and their broad range of applicability have only recently been appreciated by theorists at large. The purpose of this review is to explain and illustrate the essential characteristics of some typical noncovariant gauges, such as the axial gauge, the planar gauge, the light cone gauge and the temporal gauge. The author's aim is to acquaint the reader not only with the basic properties of these ghost free gauges, but also with their deficiencies and advantages over covariant gauges, their computational idiosyncracies, and their dominant areas of application.
Light-cone lattice approach to fermionic theories in 2D: The massive Thirring model: C. Destri and H. J. de Vega, Nucl. Phys. B290 [FS20] 363 (1987). Abstract Two-dimensional fermionic field theories are defined on a diagonal lattice obtained by discretizing Minkowski space time in light cone coordinates. This approach leads to local second quantized equations of motion on the lattice. The continuum limit is carefully performed, yielding the massive Thirring model whenever fermions without internal structure are considered. The exact eigen states and eigenvalues constructed in this lattice formalism confirm the known Bethe ansatz equations of the massive Thirring model. The light cone lattice approach brings a class of integrable fermion models within the general algebraic scheme of quantum inverse scattering method.
Light-meson distribution amplitude: Simple relativistic model: Z. Dziembowski and L. Mankiewicz, Phys. Rev. Lett. 58, 2175 (1987). Abstract With the basic concepts of the constituent-quark model formulated in the light-cone Fock approach we present a relativistic model of the pion and the -meson valence-quark structure. We point out that a nonstatic relativistic spin wave function and small transverse size of the valence configuration are essential to reproduce the basic features of the Chernyak-Zhitnitsky amplitudes for the and as they are obtained from QCD sum-rule techniques.
Nonperturbative extension of the light front QCD: J. M. Namyslowski, U. of Md. preprint, January 1987 Abstract An approximate account of the soft field fluctuations in hadrons is proposed in the framework of light front dynamics. Hadrons are considered as bound systems of constituent quarks and gluons which acquire running masses due to the interaction with soft fields. The lower bounds on the virtuality of the single hard particle give upper bounds on the quark and gluon masses: , and . The state of the hadron with momentum has virtuality , where M is the hadron mass. In the n-constituent state each constituent has average virtuality which is bounded from below. This bound gives the upper bounds on the number n of constituents in the state with virtuality : . For the hadron's bound state equation we find the n-body propagator and the irreducible kernels in terms of Jacobi relativistic relative momenta.
Nucleon properties with running quark masses: M.J. Lavelle, E. Werner, and S. G azek, Few-Body Systems, Suppl. 2, 519 (1987). Abstract The effects of quark condensate induced running quark masses upon hadronic properties are investigated. The masses are shown to lead to a self-consistency condition which bounds the masses of the quarks from above. Numerical results showing a decreasing d/u ratio are presented. The accuracy of the collinear approximation for is questioned.
Renormalization of the Yang-Mills theories in the light-cone gauge: A. Bassetto, M. Dalbosco, R.Soldati, Phys. Rev. 36D, 3138 (1987). Abstract The structure of the renormalization of the Yang-Mills theories in the light-cone gauge is investigated. It is shown that, despite the appearance of an infinite number of nonlocal divergent terms, the theory can be made finite to any order in the loop expansion by introducing a finite number of renormalization constants. Those constants can be interpreted as coefficients of a canonical transformation of fields and coupling constants in such a way that gauge invariance and unitarity of the renormalized theory are manifestly satisfied. In particular it is shown that the nonlocal structures are completely decoupled from the physical quantities.
Solving by discrized light front quantization: A. Harindranath and J. P. Vary, Phys. Rev. D 36, 1141 (1987). Abstract The recently proposed discretized light front quantization (DLFQ) method is applied to field theory in 1+1 dimensions. We start with the normal ordered Hamiltonian and perform calculations with and without finite mass renormalization in order to elucidate its role. We find that finite mass renormalization prevents the phase transition by restricting the theory to the weak coupling region. Comparison with results obtained without mass renormalization demonstrates that both treatments can yield the same estimate of the critical coupling for which the mass gap vanishes. This DLFQ estimate of the critical coupling may be compared with the analytical result. The invariant mass of various states is calculated as a function of bare coupling. In the weak coupling region where we can easily extrapolate to the continuum limit we find evidence for scattering but there is no two-particle bound state in agreement with the well known result established for constructive quantum field theory. In addition, we find no multiparticle bound states.
Structure of the perturbative chiral anomaly in the light cone gauge: Q. Ho-Kim, L. Marleau and P. Mathieu, Phys. Rev. D35, 1429 (1987). Abstract It is shown that the axial QED anomaly can be consistently calculated in the light cone gauge and the result is independent of the prescription used to treat the light cone singularities; it is found that a prescription is not even necessary. The relation between the results obtained from the two-component and the four component formulations of the light cone gauge is discussed.
The vacuum on null planes: G.N. Fleming, Presented to 1987 Oxford Univ. Symposium on the Vacuum in Quantum Field Theory, Pennsylvania State University preprint, June 1987.
Charge form factors of quark-model pions: P. L. Chung, F. Coester, and W. N. Polyzou, (1988). Abstract We demonstrate that Poincare invariant quark models of the pion can give charge form factors in agreement with all available data. The quark-antiquark model wave functions are spin-zero eigenfunctions of the four-momentum. The relativistic features of the model are essential for the result. The confinement scale is much smaller than the charhe radius.
Hamiltonian light-front dynamics of elastic electron-deuteron scattering: P. L. Chung, F. Coester, B. D. Kiester, and W. N. Polyzou, Phys. Rev. C (1988). Abstract Relativistic calculations of elastic electromagnetic form factors of the deuteron are presented for momentum transfers up to 8. Standard nucleon-nucleon interactions are used to construct a unitary representation of the inhomogeneous Lorentz group on the two-nucleon Hilbert space. Deuteron wave functions represent eigenstates of the four-momentum operator. Existing parametrizations of measured single-nucleon form factors are used to construct a conserved covariant electromagnetic current operator and the deuteron wavefunctions. The results are compared to experiment. The size of relativistic effects, scaling behaviour, sensitivity to the nucleon-nucleon interactions, and effects of the uncertainties in measured nucleon form factors are investigated.
Hard nuclear processes and microscopic nuclear structure: L. Frankfurt and M. Strikman, Phys. Rep. 160, 235 (1988). Abstract Methods to test QCD-inspired theoretical ideas on microscopic nuclear structure, in high energy hard lepton-nucleus reactions, are reviewed. Special attention is given to options at existing facilities and at facilities that will come into operation in the early nineties (the jet facility at PEP and CEBAF) The importance of light cone dynamics, the physics of large longitudinal distances, and the presence of point-like quark-gluon configurations in hadrons for the theoretical description of high energy processes (and especially nuclear shadowing) is explained. Ways to investigate the interactions between perturbative and nonperturbative QCD in nuclear shadowing are suggested. Options for probing the hard scattering wave functions of hadrons are analysed.
Light cone quantization for massless fields: G. McCartor, Z. Phys. C 41, 271 (1988). Abstract When the light cone quantization procedure is applied to massless fields care must be taken or the resulting theory will not be isomorphic to the equivalent theory quantized at equal times. The special considerations necessary for massless fields are described here and their application to recently presented calculations in 1+1 dimensions are discussed.
Light front Hamiltonian approach to relativistic two and three body bound state problems in 1+1 dimensions: A. Harindranath and J. P. Vary, Phys. Rev. D37, 1064 (1988). Abstract We utilize the Hamiltonian approach to the light front formulation of quantum field theory to study two and three body relativistic bound state problems in a truncated Fock space basis in 1+1 dimensions. The problem is numerically solved by diagonalizing the invariant mass operator in the truncated basis. We present results for binding energies, valence wave functions and the momentum distribution functions. We discuss the advantages of the present technique over the usual integral equation approach.
Light front QCD in the vacuum background: St. Glazek, Phys. Rev. D38, 3277 (1988). Abstract It is shown that the canonical light front formulation of QCD is able to incorporate ideas used by Shifman, Vainshtein, and Zakharov to successfully describe many features of the hadronic spectrum in their sum rules. It is pointed out that the new light-front Hamiltonian may lead to a quantitative model for the structure of hadrons.
Multiloop integrals, counterterms, and renormalization of Yang-Mills theories in the light-cone gauge: H. Skarke and P. Gaigg, Phys. Rev. 38D, 3205 (1988). Abstract We analyze some properties of higher-loop Feynman integrals and prove a theorem concerning their structure. With the help of this information and with ``extended Becchi-Rouet-Stora symmetry'' we perform the renormalization of Yang-Mills theory in the light-cone gauge to all orders.
Nucleon wave function with running quark masses: S. G azek and J.M. Namyslowski, Acta Phys. Polonica B19, 569 (1988). Abstract Three-quark nucleon wave function is constructed within the light-front framework. Quarks have running masses, which interpolate between the constituent and the current quark mass. In the spinor part of our model wave function all three Ioffe spin structures are needed. They are also required in the nucleon spinor currents in the QCD sum rules, if one asks for the maximal overlap with the state of the physical nucleon. In our calculations, the presence of three Ioffe spin structures is necessary to get simultaneously the negative value for the neutron charge radius and the decreasing d/u ratio in proton, which are well established experimental results. Selecting the coefficients in front of the Ioffe spin structures as: 1, 1.4 and 2.3, and the shape of Gaussian distribution in the transverse momenta about 40% broader than that of the Isgur and Karl model, we get: fm, fm, , and the decreasing d/u ratio in proton's deep inelastic scattering, if is increasing toward 1.
Null-plane formulation of Bethe-Salpeter qqq dynamics: Baryon mass spectra: D. S. Kulshreshtha and A. N. Mitra, Phys. Rev. D37, 1268 (1988). Abstract The Bethe-Salpeter (BS) equation for a qqq system is formulated in the null plane approximation (NPA) for the BS wave wavefunction, as a direct generalization of a corresponding QCD-motovated formalism developed earlier for systems. The confinement kernel is assumed vector type for both and qq pairs, with identical harmonic structures, and with the spring constant proportional, among other things, v: to the running coupling constant , (for an explicit QCD motivation). The harmonic kernel is given a suitable Lorentz invariant definition [not ], which is amenable to NPA reduction in a covariant form. The reduced qqq equation in NPA is solved algebraically in a six-dimensional harmonic oscillator (HO) basis using the techniques of SO(2,1) algebra interlinked with symmetry. The results on the nonstrange baryon mass spectra agree well with the data all the way upto N=6, thus confirming the asymptotic prediction characteristic of vector confinement in HO form. There are no extra parameters beyond the three basic constants () which were earlier found to provide excellent fits to meson spectra .
One-loop three-gluon vertex and power counting in the light-cone gauge: A. Suzuki, Z. Phys. C - Particles and Fields 38, 595 (1988). Abstract The divergent part of the one-loop three-gluon vertex is evaluated in the framework of the two-component formalism for the light-cone gauge. The result is consistent with multiplicative renormalizability for pure Yang-Mills gauge theories. The calculation entails a discussion on some of the peculiar properties of naive power counting exhibited by this special gauge. I employ the Mandelstam prescription implemented via dimensional regularization to regulate Feynman integrals.
Relativistic model of nucleon and pion structure: Static properties and electromagnetic soft form factors: Z. Dziembowski, Phys. Rev. D37, 778 (1988). Abstract I have studied the valence-quark system in a light-cone version of the constituent-quark model. A relativistic description is derived by applying light-cone boosts to model wave functions at rest which describe a valence system with the standard quark-model assignmentsof the usual constituent-quark mass, and a universal hadronic scale. With the scale fixed by static properties at 320 MeV, we find that the relativistic constituent-quark model offers an excellent description of the hadron electromagnetic form factors up to , but at larger scales is invalid.
Solvable light front model of a relativistic bound state in 1+1 dimensions: M. Sawicki and L. Mankiewicz, Phys. Rev. D37, 421 (1988). Abstract The bound state equation at equal light front time is investigated in the framework of a scalar field model in one space and one time dimension in the limit of an infinitely massive exchanged boson. Analytic expressions for the bound state mass and the form factor are obtained. In a weak binding limit the results for mass and wave function coincide with those based on the nonrelativistic Schrodinger equation with a -type potential. For weakly bound systems the form factor reduces to the proper static limit in the whole domain of momentum transfers. In general, the quality of the static approximation is controlled by a dimensionaless parameter /m that characterizes the strength of the binding.
Stability of the vacuum in scalar field models in 1+1 dimensions: A. Harindranath and J. P. Vary, Phys. Rev. D37, 1067 (1988). Abstract Utilizing the recently proposed discretized light front quantization (DLFQ) method we evaluate the critical coupling for vanishing mass gap (with respect to the perturbative vacuum) for two interacting scalar field models in 1+1 dimensions. Our extrapolated results for the critical coupling are compared with results based on equal time formulation.
The 2-dimensional light-cone integrals with momentum shift: A. Suzuki, J. Math. Phys. 29, 1032 (1988). Abstract A class of light-cone integrals typical to one-loop calculations in the two-component formalism is considered. For the particular cases considered, convergence is verified though the results cannot be expressed as a finite sum of elementary functions.
Uniqueness of the relativistic nucleon state: Z. Dziembowski, Phys. Rev. D37, 768 (1988). Abstract Within the basic concepts of the constituent-quark model formulated in the light-cone Fock approach I examine the general symmetry properties of the relativistic nucleon wave function. With these symmetry restrictions I develop an economical parametrization of the nucleon wave function expanding it in terms of known spinor amplitudes multiplied by certain unknown momentum wavefunctions. I also present a simple model of a relativistic spin wave function which fixes the expansion coefficients and leaves us with nucleon-ground-state-model wave function uniquely determined. Such a relativistic model serves as a basis for a unified description of low- and high-momentum-transfer nucleon properties presented in the following paper.
Variational calculation of the spectrum of in light front field theory: A. Harindranath and J. P. Vary, Phys. Rev. D37, 3010 (1988). Abstract We demonstrate that a coherent state may be a valid vacuum in light front field theory. Then by minimizing the sum of the expectation values of the light front Hamiltonian and the momentum operators in a variational trial state, we evaluate the ground state (vacuum) of field theory. The resulting expectation value in the coherent state is identical with the result of the effective potential method in the equal time formulation. Thus we demonstrate how to solve for the ground state of strong coupling problem on the light front. We also discuss the calculation of excited states.
Hadron Spectroscopy and Form Factors at Quark Level: S. Chakrabarty, K. K. Gupta, N. N. Singh and A. N. Mitra, Progress in Particle and Nuclear Physics, Vol. 22, ed., A. Faessler, Pergamon Press, (1989) Abstract The theoretical status of hadrons as quark composites is examined from the point of view of a simultaneous understanding of their on shell (mass spectra) and off shell (form factors, transition amplitudes) properties. To that end we first offer a perspective view of the emerging view of quark physics since the seventies, preceeded by a quick overview of some important ideas and models in the pre QCD phase that were to determine the shape of the subsequent (post QCD) developements. The primary emphasis is on theoretical approaches to effective confinement (pending a formal resolution of the confinement problem within a QCD Lagrangian framework, lattice or otherwise), in providing a fuller perspective from high to low energy physics or vice-versa. To that end greater stress is laid on light quark systems which are more sensitive to the confinement regime, and more prone to relativistic effects than on heavy quarkonia (on which many reviews exist).
The broad theoretical approaches obeying Lorentz and gauge invariance are identified: (i) QCD sum rules as a means of extrapolation from high to low energies; and (ii) dynamical equations for providing a microcausal link in the opposite direction (from low to high energies). The latter represents the major focus of attention in this article, with the Bethe-Salpeter equation (BSE) providing a formal plank for a comparitive assessment of several models. The null plane ansatz which facilitates the reduction of the 4-D BSE to a covariant 3-D form also provides the language for its comparison with other covariant 3-D equations. In particular, attention is drawn to the interesting possibility of reconstructing the 4-D BS wave Te*wfunction from its 3-D form (in a two-tier fashion) as a practical tool for generating higher Fock space components effects) in the BS wavefunction, and (more interestingly) for a clean seperation between soft and hard QCD effects.
To illustrate one such practical tool for an integrated view of different hadronic sectors within a single hadronic framework, the results of a two-tier BS model are presented in respect of , qq, gg, states and compared with experiment as well as with the results of other contemporary models. The N.R Resonating Group Method, which becomes necessary for bigger (six-quark) systems is briefly discussed from the point of view of its compatibility with a relativistic form of quark dynamics motivated from the BSE.
Light-cone gauge Schwinger model: G. McCartor, Mission Research Corporation preprint, August 1989.
Light cone quantization and manifestation of non-perturbative vacuum properties for scalar field theory: Th. Heinzl, St. Krusche, and E. Werner, Z. Phys. A334, 443 (1989). Abstract For a quantum field theory with interacting scalar fields treated in light cone quantization (LCQ) it is shown that the vacuum of the theory is always the perturbative vacuum. The fields are split into classical constant fields, determined by minima of the effective action, and quantum fields. The former ones replace the nontrivial vacuum expectation values of the conventionally quantized theory. When spontaneous symmetry breaking occurs the classical fields are only determined upto symmetry transformations. This degeneracy corresponds to the degeneracy of the vacuum in the conventional approach. The effective actions of the conventional theory and LCQ are identical. Light cone charges obey the canonical commutation relations with the fields and the canonical charge algebra relations. Ward identities and the appearence of Goldstone Bosons accompanying spontaneous symmetry breaking can be derived in analogy to the conventional case.
Light cone quantization on the lattice: D. Mustaki, Phys. Rev. D38, 1260, (1989). Abstract Field theories are regularized by discretization of the light cone coordinates. As an example, the scalar field quantization is carried in detail, and the application to Monte-Carlo computations is discussed.
Light front quantization study of two dimensional scalar field models: J. P. Vary and A. Harindranath, in Nuclear and Particle physics on the light cone, Proceedings of the LAMPF Workshop, Los Alamos, New Mexico, 18-22 July, 1988, eds., M. B. Johnson and L. S. Kisslinger, World Scientific, Singapore, (1989). Abstract With the aim of understanding the features of light front quantization we have studied two-dimensional scalar field models. In this work we present a brief overview of the subject and a summary of our results. In particular we address the issue concerning the nature of the physical vacuum in light front field theory.
Light front variational approach to scalar field theories: E. A. Bartnik and St. Glazek, Phys. Rev. D39, 1249 (1989). Abstract We present a variational method of estimating the ground state energy for quantum field theories on the light front in an arbitrary number of dimensions. For scalar fields, variational parameters are the constant background field and the boson mass. In this case our method is equivalent to the standard equal time method.
Numerical solution of the one-pair equation in the massive Schwinger model: Y. Ma and J. R. Hiller, J. Comp. Phys., 82, 229 (1989). Abstract We describe various numerical methods for the solution of the one pair light cone equation in the massive Schwinger model. Results obtained by thses methods, and by others, are compared. Possible extensions to the coupled set of one-pair and two-pair are discussed.
Quantizing QED on the light cone: T. Eller and H. C. Pauli, Z. Phys. C42, 59 (1989). Abstract The method of discretized light cone quantization (DLCQ) is applied to quantum electrodynamics in one space and one time dimension (QED) with different initial conditions. This leads to different representations of the operators of the constants of motion. Within the fermion-antifermion approximation we perform analytically the transition to the continuum limit and show that the discrete massive and massless representations are equivalent. We compare a semiclassical calculation of the number of bound states with results obtained in the continuum limit. Furthermore a discrete bosonized version of QED is discussed.
Relativistic bound systems in QED: S. I. Nagornyi, Yu. A. Kasatkin, E. V. Inopin and I. K. Kirichenko, Sov. J. Nucl. Phys. 49, 465, (1989). Abstract The covariant formulation of field theory is used to develop a Lorentz and gauge invariant approach to the description of electromagnetic processes on nuclear systems with consistent allowance for their internal structure. The transition to dynamics on the light front hypersurface is considered.
Scattering of composite particles in a gauge theory with confinement: J. F. Briere and H. Kroger, Phys. Rev. Lett. 63, 848 (1989). Abstract In order to model positronium-positronium scattering in QED or meson-meson scattering in QCD, we consider QED, which is a gauge theory and confines single fermions. We present the first numerical results of a lattice calculation on the scattering of two composite particles. The composite particles are taken as neutral, fermion-antifermion, lowest mass eigenstates of the Hamiltonian. We use the light cone momentum representation on a lattice and employ a nonperturbative time-dependent method to compute the S-matrix.
Solvable light-front model of the electromagnetic form factor of the relativistic two-body bound state in 1+1 dimensions: L. Mankiewicz and M. Sawicki, Phys. Rev. D40, 3415 (1989). Abstract Within a relativistically correct yet analytically solvable model of light-front quantum mechanics we construct the electromagnetic form factor of the two-body bound state and we study the validity of the static approximation to the full form factor. Upon comparison of full form factors calculated for different values of binding energy we observe an unexpected effect that for very strongly bound states further increase in binding leads to an increase in the size of the bound system. A similar effect is found for another quantum-mechanical model of relativistic dynamics.
Symmetry breaking in the two dimensional theory and the light front vacuum: R. S. Wittman, in Nuclear and Particle physics on the light cone, op. cit. Abstract The scalar field theory in 1+1 dimensions is considered in the descretized light cone quantization approach. The approach is redeveloped through the Lagrangian rather than the energy-momentum transfer. The special role of the zero-mode (zero light cone momentum) coordinate appears through a nonlinear constraint equation involving the standard nonzero light cone momentum Fock space creation and annihilation operators.
The applicability of perturbative QCD to exclusive processes: N. Isgur and C. H. Llewellyn Smith, Nucl. Phys. B317, 526 (1989). Abstract We re-examine our arguments against the dominance of perturbative QCD over soft, non-perturbative effects in exclusive processes at currently available . We continue to find that perturbative contributions are much smaller than soft contributions (which are capable of explaining the data) in the sample test cases of the pion and nucleon electromagnetic form factors. We see no reason why our results should not generalize, and conclude that there is no justification for the continued application of perturbative QCD for exclusive processes.
The cancellation of nonlocal divergences in light-cone theories: O. Piguet, G. Pollak, and M. Schweda, Nucl. Phys. B328, 527 (1989). Abstract The nonlocal divergences arising in gauge theories quantized in the light-cone gauge are regularized with the help of a ``cut-off'' playing the role of a gauge parameter. It follows from the nonphysical character of this parameter that the nonlocal divergences drop out in the physical quantities. The result is valid to all orders of perturbation theory and does not require the existence of any invariant regularization scheme. Our considerations are based on an extended BRS-symmetry.
The fermion condensate of the Nambu-Jona-Lasinio model in light cone quantization: C. Dietmaier, T. Heinzl, M. Schaden and E. Werner, Z. Phys. A334, 215 (1989). Abstract We investigate the incorporation of condensates in Light cone quantization in the framework of Nambu-Jona- Lasinio model. Although it is shown that the physical and perturbative vacua are identical, a gap equation for the dynamical quark mass is obtained and chiral symmetry is dynamically broken. The complete fermion condensate is found in the perturbative vacuum. The corresponding Goldstone mode is a zero mass bound state Weinberg equation.
The virial theorem and the structure of the deuteron in 1+1 dimensional QCD on the light cone: M. Burkardt, Nucl. Phys. A504, 762 (1989). Abstract The spectrum and the structure functions of hadrons in QCD are investigated. Special emphasis is put on the question of sea quark admixtures in ground state hadrons. A nonperturbative theorem is derived which relates the minus 2nd moments of the structure functions to hadron masses and thereby predicts suppression of the nuclear structure function in the small x region.
A new picture for light front dynamics: M. G. Fuda, Ann. Phys. 197, 265 (1990). Abstract A new picture for light front dynamics is developed which employs an arbitray, external, light like four vector . The state vectors and operators in this so called picture are related to the state vectors and operators in the standard formulation of light front dynamics by a unitary transformation which depends on the unit vestor , where is the three vector part of . This unitary transformation is somewhat analogous to the transformation which relates the Heisenberg picture to the interaction picture, with two angles that specify the direction of playing the role of the time. Just as the interaction picture is designed to cope with the interaction in the Hamiltonian, the picture is designed to cope with the interaction in the angular momentum operator . In this picture the action of the angular momentum operator is equivalent to the action of , where is the noninteracting part of and is an orbital angular momentum operator. The standard theory of angular momentum can be used to to construct eigenstates of and ; however, some of these states are spurious. The physical states can be obtained by imposing a dynamical constraint equation. A momentum representation for the picture state vectors and operators is developed. It is shown that the wavefunctions for states of well-defined total four-momentum factor into an invariant function and a function which depends on relative three momentum variables and a unit vector , which is in a cm frame. Under a Lorentz transformation, the transformation of state vector is equivalent to a three rotation of the 's and . The general formalism is applied to a model which describes a two-particle system for which there exists manifestly covariant wavefunctions of the space-time variables for the two particles. The covariant wavefunctions satisfy the standard constraint of covariant constraint dynamics.
Ab initio quantum chemistry: a source of ideas for lattice gauge theorists: K.G. Wilson, Nucl. Phys. B (Proc. Suppl.) 17, 82-92 (1990). Abstract Ab initio quantum chemistry is an emerging computational area that is fifty years ahead of lattice gauge theory, a principal competitor for supercomputer time, and a rich source of new ideas and new approaches to the computation of many fermion systems. An overview of the history, current prospects and future frontiers of quantum chemistry is given, with special emphasis on lessons for lattice gauge theory. Particular reference is given to the role of Gaussian basis functions (in place of grids) and analytic (as opposed to Monte Carlo) methods. The main recommendation to lattice gauge theorists is for greater emphasis on infinite momentum frame studies, using Gaussian basis functions.
Angular momentum constraints in the light-cone quantum mechanics of the nucleon-nucleon system: L. L. Frankfurt, M. I. Strikman, L. Mankiewicz and M. Sawicki, Few Body systems, 8, 37 (1990). Abstract We show that in the framework of the light-cone quantum mechanics of the two-nucleon system the constraints due to anglar momentum conservation can be reconstructed from the requirement of Lorentz invariance of the on-mass- shell scattering amplitudes. We have reduced the problem to the analysis of the rotational invariance of a Lippmann-Schwinger type equation and we show that, under plausible assumptions, maintatining rotational invariance of the scattering amplitude requires the two-body potential to be rotationally invariant.
Constructing hadrons on the light cone: K. Hornbostel, Proceedings of the Workshop, From Fundamental Fields to Nuclear Phenomena, Boulder, CO, Sept. 20-22, 1990, Ed. J.A. McNeil and C.E. Price. Abstract This talk is an introduction to some of the advantages and peculiarities of light-cone quantization. It compares the steps needed to compute hadronic states on the light cone versus those needed with conventional equal-time quantization, emphasizing the simplicity of boosts and of the vacuum in the light-cone formalism.
Discretized light cone quantization in a 3+1 dimensional valence model for quarkonium: D. Klabucar and H. C. Pauli, Z. Phys. C47, 141 (1990). Abstract Led by the successes of the nonperturbative method of discretized light cone quantization (DLCQ) in 1+1 dimensional toy models, we study the feasibility of extending to 3+1 dimensional theories. Within a SU(N) nonabelian gauge theory, DLCQ is applied to a quarkonium system, where the Fock space has been truncated to the valence quark and antiquark only. In the light cone gauge the valence model Hamiltonian matrix has an interesting structure which enables us to reduce the problem of diagonalization of some extremely large matrices to an amount of numerical labor already coped with in 1+1 dimensions. The model spectrum and the eigenfunctions are calculated independent of the order of the nonabelian gauge group, in special cases even analytically. The type of spectrum which appears after the calculation has been regularized covariantly may be interpreted as a sign that the quarks are confined in this model.
Gauge theories in the light-cone gauge: K. Haller, Phys. Rev. D42, 2095 (1990). Abstract A canonical formulation, using equal-time commutation rules for canonically conjugate operator-valued fields, is given for quantum electrodynamics and Yang-Mills theory in the light-cone gauge. A gauge-fixing term is used that avoids all operator constraints by providing a canonically conjugate momentum for every field component. The theory is embedded in a space in which the light-cone gauge condition and all of Maxwell's equations hold. Interaction picture fields and the photon and gluon propagators in the light-cone gauge are evaluated for two alternate representations of the longitudinal and timelike components of gauge fields. One representation makes use of the entire momentum space to represent these gauge field components as superpositions of ghost annihilation and creation operators. The other uses only ghost excitations with for the longitudinal modes of , but restricts the gauge-fixing field to ghost excitations with . It is shown that the former mode leads to a formulation that corresponds to the principal-value (PV) prescription for the extra pole in this gauge, the latter to the Mandelstram-Leibbrandt (ML) prescription. Nevertheless the underlying theory for these two cases is identical. In particular, for QED both modes give identical time evolution, within a physical subspace in which constraints are implemented, as does QED in the Coulomb gauge. It is therefore concluded that canonical formulations of the light-cone gauge cannot be a basis for preferring the ML to the PV prescription for the extra pole at in the light-cone propagator.
Hamiltonian formulation of two-dimensional gauge theories on the light-cone: F. Lenz, Hadrons and Hadronic Matter, 119 (1990). Abstract In Quantum Chromodynamics, the theory of strong interactions, gluons and quarks are the microscopic degrees of freedom. Hadrons constitute the effective degrees of freedom in terms of which hadronic and nuclear reactions as well as nuclear structure are traditionally described. The fundamental problem of low energy strong interaction theory is to understand, within the framework of QCD, the transition from microscopic to phenomenological degrees of freedom. Quark models have been important in clarifying this relation between microscopic and effective degrees of freedom as far as the structure of single hadrons is concerned. As the historical development already indicates, compositeness together with a simple picture about the underlying confining dynamics is sufficient for a qualitative understanding of hadronic properties in terms of ``constituent'' quarks.
Is light front quantum field theory merely a change of coordinates?: D.V. Ahluvalia and D.J. Ernst, An earlier version published on D. Ahluwalia, in ``HUGS at CEBAF, 1990 - Proceedings'' 179-195, 1990. Abstract The free particle Dirac equation is solved in the instant form using a new set of coordinates. One limit of the solutions is the usual instant form results while a different limit allows one to asymptotically approach the light front. By also solving the Dirac equation on the light front, we are able to compare and contrast the logic of the two approaches. Although no answer is given to the question posed in the title, the generalized instant form of the dynamics presented offers a new way of formulating the problem and we provide some thoughts on some of the basic conceptual differences between the two approaches.
Light-cone gauge and the (causal) principal-value prescription: B.M. Pimentel and A.T. Suzuki, Phys. Rev. D42, 2115 (1990). Abstract The principal-value (PV) prescription constrained with causality is used to treat the unphysical pole in the basic one-loop light-cone integral. It is shown that the so-modified prescription avoids the emergence of double-pole singularities, contrary to what has been previously obtained in the PV scheme without causality. However, there remains an overall factor which does not agree with the results derived in the Mandelstam-Leibbrandt (ML) prescription. This overall factor is a remnant coming from the definition of the prescription proper.
Light-cone quantized QCD in 1+1 dimensions: K. Hornbostel, S. J. Brodsky, and H.-C. Pauli, Phys. Rev. D41, 3814 (1990). Abstract The QCD light-cone Hamiltonian in one space and one time dimension is diagonalized in a discrete momentum-space lattice. The hadronic spectrum and wave functions for various coupling constants, numbers of color, and baryon number are computed.
Light front Tamm-Dancoff field theory: Robert J. Perry, Avaroth Harindranath and Kenneth G. Wilson, Phys. Rev. Lett. 65, 2559 (1990). Abstract Light front field theory may provide a promising avenue of research for nuclear and particle physics, but a Tamm-Dancoff truncation of field theory is required for practical computations. Such a truncation limits the number of virtual mesons allowed in hadronic field theories, or the number of quarks and gluons allowed in bound states described by quantum chromodynamics. Past renormalization problems with Tamm-Dancoff methods are analyzed and a solution for these problems is proposed.
Meson properties in a light cone quark model: Nihal A. Aboud and John R. Hiller, Phys. Rev. D41, 937 (1990). Abstract A potential with three parameters is used in a light cone equation for a quark-antiquark pair. Spin dependence is not included. The nonrelativistic limit is the potential of the quark model of Eichten et al. Numerical methods are used to solve the eigenvalue problem. The parameters and quark masses are varied to obtain a reasonable fit to masses of low-lying hidden-flavor mesons. Additional masses are calculated for higher states and for flavored mesons. Also, properties of the pion are calculated from a wavefunction obtained with the numerical method. Spectroscopic assignments are problematic because the light front formulation breaks rotational invariance. A need for an improved treatment of angular momentum eigenstates are indicated.
Multiquarksysteme in der 1+1 dimensionalen QCD: M. Burkardt.
Null-plane Bethe-Salpeter dynamics: mass spectra, decay constants of pseudoscalar mesons, and the pion form factor: K.K. Gupta, A.N. Mitra, and N.N. Singh, Phys. Rev. D42, 1604 (1990). Abstract A new relativistic definition of the reduced mass of a pair, so as to be in conformity with the standard Wightman-Garding definition of its relative four-momenta , is introduced into the kernel of an ongoing Bethe-Salpeter (BS) program on a two-tier basis. The new definition of (involving the hadron mass M) is found to produce a natural Regge asymptotic behavior in the hadron mass spectra, while retaining the property of an asymptotically linear confinement in the three-dimensional structure of the BS kernel. The relativistic structure of is responsible for a significant improvement in the fits to the ground-state masses of and mesons as compared to its nonrelativistic definition . The leptonic decay constants and the charge radii thus calculated are also in excellent agreement with data where available, while predictions for mesons have good overlap with recent lattice predictions. Further, the scaling property of the hadron's electromagnetic form factor at large is a consequence of the ``on-shell'' form of its null-plane wave function. All these results (which are indicated in the barest outline) are preceded by a perspective summary of the theoretical premises and practical working of the BS equation with a four-fermion interaction kernel as a necessary background on a two-tier basis.
Null plane quantization of fermions: D. Mustaki, Phys. Rev. D42, 1184 (1990). Abstract Massive Dirac fermions are canonically quantized on the light cone using the Dirac-Bergmann algorithm. The procedure is carried out in the framework of QED as an illustration of a rigorous treatment of interacting fermion fields.
Relativistic bound-state form factors in a solvable (1+1)- dimensional model including pair creation: St. Glazek and M. Sawicki, Phys. Rev. D41, 2563 (1990). Abstract The relativistic two-body bound state form factor, recently calculated by Mankiewicz and Sawicki from a light front formula involving analytic solutions to the Weinberg equation in a 1+1 dimensional model field theory, is compared with the form factor obtained from the Mandelstam formula using analytic solutions to the corresponding Bethe-Salpeter equation. The results are different, since the former formula does not include the contribution of pair-creation diagrams which are included in the latter. When the pair-creation diagrams are included in the light-front formula in 1+1 dimensions, both approaches yield a numerically identical form factor, not having the strange properties described by Mankiewicz and Sawicki.
Rotational symmetry in the relativistic constituent quark model: H. J. Weber, Phys. Rev. C42, 461 (1990). Abstract Nucleon matrix elements at zero momentum transfer of the relativistic constituent quark model on the light cone, where rotational symmetry is only approximate, are shown to reproduce the characteristic ratios 3, 1, and of the Wigner-Eckart theorem based on rotational isospin invariance.
Simple relativistic quark-model analysis of flavored pseudoscalar mesons: C. -R. Ji and S. R. Cotanch, Phys. Rev. D41, 2319 (1990). Abstract Using a simple relativistic quark model suggested by Dziembowski et al., we study the open flavored pseudoscalar meson, i.e., where Q is s or c and q is u or d. Our analysis which is a straightforward extension of their previous treatment for the pion, focusus on the kaon to provide further tests of this approach. Our results supports the utility of this model as the predictions for the kaon charge radius , the kaon form factor , and the decay constant compare favorably with experimental data.
Soft-pion theorems and a light-cone quark model: Z.J. Cao and L.S. Kisslinger, Phys. Rev. Letts. 64, 1007 (1990). Abstract It is shown that in a light-cone representation of nucleons soft-pion theorems which are violated in instant-form quark models can be recovered with suitable choices of parameters of the model. Instantaneous terms must be included for the soft-pion limit. The proton form factors are fit up to (GEV/c) in this model.
A Hamiltonian formulation of QED on the light cone: M. Burkardt and A. Langnau, Phys. Rev. D44,1187 (1991). Abstract It is shown that an improper regularization in the light-cone quantization of field theories can introduce a violation of rotational invariance as well as spurious divergences. Several methods are developed to avoid or cure these problems, as required for a consistent renormalization procedure of gauge theories. Based on these methods, the light-cone Hamiltonian for is constructed. Extension to gauge theories in 3+1 physical dimensions is also discussed.
An equal-time quantized field theory on the light cone: D.G. Robertson and G. McCartor, Southern Methodist University preprint, SMUHEP/91-03. Abstract The isomorphism between the equal-time and light-cone Fock space representations of the scalar-coupled Yukawa theory in 3+1 dimensions is constructed to lowest order in perturbation theory. The light-cone vacuum is shown to be the physical vacuum state of the theory, and the equal- commutation relations between the fields are determined. The dynamical operators are shown to be correctly given by components of the energy-momentum tensor integrated over the surface .
Angular momentum and light-front scattering theory: M.G. Fuda, Phys.\ Rev. D44, 1880 (1991). Abstract The role of the Leutwyler and Stern spin operator in the angular momentum analysis of light-front scattering theory is analyzed. The equations of formal scattering theory are transformed to the picture using the unitary operator recently developed by the author. This operator depends on the two angles which determine the direction of the three-vector part of a lightlike four-vector . It is shown that an invariant version of light-front perturbation theory developed earlier by the author is related to the standard theory by the unitary operator . It is also shown how to carry out a partial-wave analysis of the Lippmann-Schwinger-like equations obtained by summing a subset of the diagrams of this invariant form of light-front perturbation theory. The analysis presented here makes clear that the picture overcomes many of the difficulties due to the interaction dependence of light-front angular momentum operators, in particular the difficulties arising from the fact that the individual diagrams of light-front perturbation theory are not rotationally invariant.
Application of discretized light-cone quantization to a field theory of charged and neutral bosons in 1+1 dimensions: J.R. Hiller, Phys. Rev. D44, 2504 (1991). Abstract The numerical technique of discretized light-cone quantization (DLCQ) is used to study a theory of a charged boson that interacts with a neutral boson through a Yukawa-type coupling. The theory is a generalization of the Wick-Cutkosky model, in the sense that both bosons are massive; however, the number of spatial dimensions is restricted to 1. The charge is treated as an internal quantum number that can be proved with an external photon. The mass-eigenvalue problem is formulated and solved, with the Lanczos algorithm used as the means of matrix diagonalization. In fact, this may be viewed as a preliminary test of the utility of the Lanczos algorithm in the context of DLCQ. Eigenvectors are obtained and then used to compute structure functions, form factors, and charge radii. The instability of the vacuum is indicated by the appearance of imaginary masses.
Approximation schemes for an electromagnetic form factor of a relativistic system: M. Sawicki, PACS numbers: 25.30.-c, 11.80.-m, 11.10.St., CTP-TAMU 06/91, Texas A&M University preprint Abstract We study the electromagnetic form factor of a simple system of two scalar particles (``nucleons'' or ``quark-antiquark'') bound to form a scalar composite system (``deuteron'' or ``meson''). The use of covariant contact interaction allows for analytic solution of the Bethe-Salpeter equation. The covariant electromagnetic form factor is constructed. Equivalent light-front and equal-time representations of the covariant form factor are given, and respective valence approximations are discussed. Several quantum mechanical approximations of wave function are also obtained and resulting form factors are constructed. Validity of all approximations is then discussed.
Boost-invariant description of nuclear matter: S. G azek and C.M. Shakin, Phys. Rev. C44, (1991). Abstract We present a self-consistent mean-field description of nuclear matter making use of light front dynamics and focus our attention on a model with nucleons coupled to scalar mesons. We derive the mean-field Dirac equation for nucleon separation energies. The nucleon-meson seagull interactions are included in the calculations. In the mean-field analysis, the nucleon momentum sum rule, which plays an important role in the description of deep-inelastic scattering from heavy nuclei, results from the thermodynamical consistency condition that there is no pressure at zero temperature. We obtain the same energy density of nuclear matter at rest as one derives in the instant form of dynamics. Our light front mean-field formalism describes nuclear matter in uniform motion at any possible velocity.
Bosonic zero modes in discretized light-cone field theory: G. McCartor and D.G. Robertson, Southern Methodist University preprint, SMUHEP/91-04. Abstract It is shown that for theories with bosonic fields a constrained zero mode is a necessary ingredient for a consistent discretized light-cone quantization (DLCQ). Inclusion of this zero mode is shown to remove a noncovariant, quadratically divergent contribution to the fermion self-energy in 3+1 dimensional Yukawa theory which would otherwise be present. It is further shown to result in a fully consistent set of Heisenberg equations. The possibility of maintaining parity in DLCQ is discussed.
Bound state problem in light-front Tamm-Dancoff: a numerical study in 1+1 dimensions: A. Harindranath, R.J. Perry, and J. Shigemitsu, The Ohio State University preprint, August 1991. Abstract Numerical solutions to the two-fermion bound state problem in the 1+1 dimensional Yukawa model are presented within the lowest order light-front Tamm-Dancoff approximation (i.e., keeping only two-fermion and two-fermion/one-boson sectors). Our motivation is twofold: First, we want to understand the dynamics of the model from the very weak coupling domain where the system is governed by non-relativistic dynamics to moderate and strong coupling domains where retardation and self-energy effects become important. Second, we want to develop techniques for solving coupled Tamm-Dancoff integral equations, in particular methods that can be generalized to higher order Tamm-Dancoff approximations and/or higher dimensional theories. To achieve the first goal we first simplify the problem considerably (from a numerical point of view) by the explicit elimination of the higher Fock space sector. The resulting integral equation, whose kernel depends upon the invariant mass of the state, is solved for the coupling constant, for a given set of the invariant mass and fermion and boson mass parameters. To achieve the second goal we solve the coupled set of equations using both basis functions and direct discretization techniques. Results from these more general techniques are compared with the explicit elimination method.
Calculation of in (1+1)-dimensional QED: application of Lanczos tridiagonalization and recursion: J.R. Hiller, Phys. Rev.\ D43, 2418 (1991). Abstract A nonperturbative technique for the calculation of the cross section for hadron production in electron-positron annihilation is considered. It is a combination of Lanczos tridiagonalization and recursion used previously by others for calculations of local densities of states that arise in condensed-matter physics. The primary advantage of the technique is that computation of the full spectrum is not required; this can reduce the computing time significantly. The steps by which the approach can be applied to hadron-production calculations are explored. As an illustration, the method is applied to a model process in 1+1 dimensions; however, the approach could be used for (3+1)-dimensional processes, including those governed by quantum chromodynamics.
Causal prescription for the light-cone gauge: B. Pimentel and A. Suzuki, Modern Phys. Lett. 8, #28, 2649 (1991). Abstract We present a prescription for light-cone gauge singularities which embeds in it causality and show that it results in simpler and less demanding integrals to be performed.
Compton scattering in the light-cone Tamm-Dancoff approximation: D. Mustaki and S. Pinsky, Ohio State University Preprint, DOE/ER/01545-568, (1991). Abstract The Tamm-Dancoff approximation is used to study Compton scattering in light-cone quantized QED. The charge one sector is considered in a two particle truncated Fock space. The problem is exactly solvable and it is shown that the internal photon propagator develops a singularity similar to the one reported in the light-cone calculation of positronium. This singularity depends on the external energy and therefore can not be removed by conventional counter terms.
Discretized light-cone quantization: formalism for quantum electrodynamics: A.C. Tang, S.J. Brodsky and H.C. Pauli, Phys. Rev. D44, 1842 (1991). Abstract A general nonperturbative method for solving quantum field theories in three space and one time dimensions, discretized light-cone quantization, is outlined and applied to quantum electrodynamics. This numerical method is frame independent and can be formulated such that ultraviolet regularization is independent of the momentum-space discretization. In this paper we discuss the construction of the light-cone Fock basis, ultraviolet regularization, infrared regularization, and the renormalization techniques required for solving QED as a light-cone Hamiltonian theory.
Discretized light-cone quantization of (1+1)-dimensional QED reexamined: C.M. Yung and C.J. Hamer, Phys. Rev. D44, 2598 (1991). Abstract We reconsider the discretized light-cone quantization of QED in 1+1 dimensions, paying particular attention to the assumptions used by Eller, Pauli, and Brodsky. One result is an alternative interpretation of confinement to that given by Eller et al.
Fixed sources in light-front dynamics and Wilson's model of coupling constant renormalization: S.D. G azek and R.J. Perry, The Ohio State University preprint, December 20, 1991. Abstract We construct a fixed source model of nonperturbative coupling constant renormalization in light-front dynamics, as a limit of a theory of heavy fermionic sources when the fermion mass becomes very large. We begin with the canonical light-front Hamiltonian for Yukawa quantum field theory. We introduce cutoffs and consider the limit when the fermion mass is much larger than the momentum cutoffs. We then derive an effective Hamiltonian in the Fock space spanned by sectors with only one fermion and arbitrarily many bosons. The total momentum of the dressed fermionic source is separated from the internal dynamics of the system. The effective Hamiltonian for the internal dynamics is shown to be equivalent to the original fixed source model Hamiltonian considered by Wilson. Wilson's nonperturbative renormalization group analysis applies to the light front version of the model. The new feature of the light-front model is the appearance of manifest boost invariance, which allows one to study a heavy fermion source with arbitrary momentum. We discuss generalization of the renormalization group analysis to the case where the fermion mass is comparable to the boson mass.
Higgs mechanism in light-front quantized field theory: P.P. Srivastava, The Ohio State University preprint, December 1991. Abstract The spontaneous symmetry breaking of continuous symmetry in light-front quantized scalar field theory is studied following the Dirac procedure for constrained dynamical systems. The zero modes are shown to commute with the non-zero ones and the isovector built from them is seen to characterize a (non-perturbative) vacuum state and the corresponding physical sector. The infinite degeneracy of the vacuum is described by the continuum of the allowed orientations of this background isovector in the isospin space. The symmetry generators in the quantized field theory annihilate the vacuum in contrast to the case of equal-time quantization. Not all of them are conserved and the conserved ones determine the surviving symmetry of the quantum theory Lagrangian. The criterian for determining the background isovector and the counting of the number of Goldstone bosons goes as in the equal-time case. A demonstration in favour of the absence of Goldstone bosons in two dimensions is also found. Finally, we extend the discussion to an understanding of the Higgs mechanism in light-front frame.
Instant form front form: collapse of spinorial degrees of freedom from and related matters: D. Ahluwalia, Center for Theor.\ Physics, Texas A&M, CTP-TAMU 87/91. Abstract Following our earlier work, a critical conceptual and mathematical study of the evolution along an arbitrary timelike direction is undertaken. Various ambiguities and subtle matters involving Dirac's front form of evolution are discussed. An ab initio solution of the Dirac equation, for evolution along an arbitrary timelike direction, is given. These solutions reduce to the standard Dirac spinors when the timelike axis is taken to be the usual time axis of the instant form. The construction of the associated conserved current turns out to be non-trivial. The conserved current is presented. This allows us to introduce gauge interactions in a straight forward fashion. A curious result, already noted by Penrose and Chang et al. in similar contexts, is once again arrived: The number of degrees of freedom for a massive spin-1/2 particle seem to collapse from as one lets the arbitrary timelike axis fall asymptotically on the light cone, and identify the resulting conclusions with the front form results. Some speculative remarks provide physical insight into the nature of singularities responsible for this collapse in the degrees of freedom.
Interpolating Dirac spinors between instant and light front forms: D. Ahluwalia, Center for Theor. Physics, Texas A&M, CTP-TAMU 88/91. Abstract Explicit expressions for the interpolating Dirac spinors needed in studies of evolution along an essentially arbitrary time-like direction are presented. One result of this work reproduces instant form results, and the other yields the light front results. The collapse of the spinorial degrees of freedom from four to two follows if we confine to a class of normalization choices.
Light-cone gauge Schwinger model: G. McCartor, Southern Methodist University preprint, SMUHEP/91-02. Abstract Nakawaki's Coulomb gauge solution to the Schwinger model is transformed to light-cone gauge. Various options for maintaining the gauge invariance necessary to satisfy the equations of motion are discussed. Satisfactory light-cone gauge solutions are found and are used to study light-cone quantization, the calculation of the dynamical operators and properties of the vacua in the light-cone representation. The solutions found here can be used to justify previous light-cone Tamm-Dancoff calculations performed by others.
Light cone quantisation of scalar field theories: T. Heinzl, S. Krusche and E. Werner, Universität Regensburg preprint, TPR 91-23. Abstract We reexamine light cone quantisation of scalar field theories with a spontaneously broken internal symmetry. To this end we use the Dirac-Bergmann algorithm for quantisation of constrained systems working in a finite spatial volume. Carefully taking into account the zero modes with light cone momentum , we obtain secondary constraints which determine the (tree level) vacuum structure of the theories. In 1+1 dimensions there is one secondary constraint which is solved by a large volume expansion. Spontaneous symmetry breaking shows up in terms of a direct sum decomposition of the Hilbert space corresponding to the discrete phases of the theory. In 3+1 dimensions, when a continuous symmetry is spontaneously broken, one finds additional first class constraints. The undetermined Lagrange multipliers are fixed by subsidiary conditions that amount to choosing a definite minimum of the potential. The application of the method to the discretised light cone quantisation approach is outlined in an appendix.
Light front dynamics of few body systems: M.G. Fuda, State University of New York at Buffalo. Abstract A brief review of light front dynamics is given, with emphasis on the interaction dependence of light front angular momentum operators. The -picture approach for dealing with this interaction dependence is outlined. The -picture employs an arbitrary lightlike four-vector . The state vectors and the operators in the -picture are related to those in the standard picture by a unitary transformation which depends on the unit vector , where is the three-vector part of . The Okubo-Glöckle-Müller approach for constructing direct interaction instant form models from quantum field theories is extended to light front dynamics in both the standard picture and the -picture. This extension is applied to a toy model of the nucleon-nucleon and pion-nucleon systems, and it is shown that a natural approximation scheme arises which leads to Poincaré-invariant potential models for these systems. The validity of the approximations is justified by means of numerical calculations of S-matrix elements.
Light front limit in a rest frame: M. Sawicki, CTP-TAMU 05/91, Texas A&M University preprint. Abstract Covariant perturbation theory is formulated using new set of space-time coordinates. This corresponds to a quantization on any flat spacelike surface in the Minkowski space. One limit of the theory reproduces the usual instant (equal time) dynamics, whereas a different limit gives a light front dynamics. Neither infinite momentum frame nor infinite momenta are involved. In particular a smooth parametric transformation from instant to light front picture is given for a system at rest.
Lowest order mass corrections for Yukawa in light front perturbation theory: A. Harindranath and Robert J. Perry, Phys. Rev. D43, 492 (1991). Abstract In this work we explicitly demonstrate the equivalence of covariant (Feynman) perturbation theory with noncovariant light front perturbation theory (LFPT) for lowest order self energy corrections in the 1+1 dimensional Yukawa model. We also perform calculations in old fashioned perturbation theory in the infinite momentum frame (OFPT) to elucidate the differences between LFPT and OFPT.
Nontrivial vacua from equal time to the light cone: K. Hornbostel, Cornell University preprint, CLNS 91/1078. Abstract Kinematic arguments suggest that the perturbative vacuum may be an eigenstate of the full Hamiltonian for light-cone quantized field theories. Nevertheless, properties such as spontaneous symmetry breaking can be accomodated in this approach, by applying a quantization which interpolates between equal-time and light-cone quantization and in which the quantization surface may approach the light cone as a limit. In several simple two-dimensional models presented here, including the Gross-Neveu and Schwinger models, the difference between the full and perturbative vacuum vanishes in this limit. Nonzero vacuum expectation values, however, are preserved by singularities in the fields near . Furthermore, this procedure provides a simple treatment for massless fields and nontrivial tests of Lorentz invariance, and may be applied to models, such as that of Gross and Neveu, for which conventional light-cone quantization is difficult to implement.
Null-plane dynamics of particles and fields: F. Coester, Argonne National Lab., PHY-6910-TH-91. Abstract The focus of this review of null-plane dynamics is the fundamental principle of quantum theory that states must form a linear manifold with a positive scalar product. The intent is to provide an integrated overview of diverse aspects of null-plane dynamics of particles and fields. Hamiltonian particle dynamics is based on the construction of nontrivial representations of the Poincaré group on finite tensor products of single-particle spaces, and on finite direct sums of such tensor products. The structure of the space of states and the representations of a kinematic subgroup are independent of the dynamics. The dynamics is specified by Hamiltonian operators which are the Poincaré generators outside the kinematic subgroup. Fock-spaces are infinite direct sums of tensor products of single particle spaces. Fock-space representations of Lagrangean field theories can be formulated as limits of Hamiltonian many-body dynamics. The required cutoff can preserve the symmetry of the kinematic subgroup but destroys the full Poincaré invariance. The nontrivial questions involve the existence of limits as the cutoff is removed. Covariant wave functions arise either as solutions of covariant wave equations, or as matrix elements of products of covariant field operators. The linear manifold of states is a manifold of equivalence classes of covariant functions. The dynamics appear in the nontrivial inner product and all Poincaré transformations are kinematic. Null-plane restrictions of the covariant functions may provide a unitary map of the covariant constraint dynamics into null-plane Hamiltonian dynamics.
On spontaneous symmetry breaking mechanism in light-front quantized field theory: P.P. Srivastava, The Ohio State University preprint, November 1991. Abstract Following the conventional Dirac procedure, we describe the spontaneous symmetry breaking in light-front quantized scalar field theory. The zero mode operator of the field is shown to commute with the nonzero mode operators, and thus may be looked upon as a background field. Its values are found by setting the first variational derivative of the potential to zero, just like in the case of equal time quantization. These values characterize the various (non-perturbative) vacua over which the corresponding physical sectors may be built by applying the non-zero mode operators.
Parton interpretation of the nucleon spin-dependent structure functions: L. Mankiewicz and Z. Ryzak, Phys. Rev. D43, 733 (1991). Abstract We discuss the interpretation of the nucleon's polarized structure function . If the target state is represented by its Fock decomposition on the light cone, the operator-product expansion allows us to demonstrate that moments of are related to overlap integrals between wave functions of opposite longitudinal polarizations. In the light-cone formalism such wave functions are related by the kinematical operator , or light-cone parity. As a consequence, it can be shown that moments of give information about the same parton wave function, or probability amplitude to find a certain parton configuration in the target which defines or . Specific formulas are given, and possible applications to the phenomenology of the nucleon structure in QCD are discussed.
Perturbative renormalization of null-plane QED: D. Mustaki, S. Pinsky, J. Shigemitsu, and K. Wilson, Phys. Rev. D43, 3411 (1991). Abstract It has been recognized for some time that quantization on a null plane has several unique and remarkable advantages for the elucidation of quantum field theories. To date these unique features have not been exploited to solve strongly coupled, four-dimensional gauge theories. This is the first in a series of papers aimed at systematically formulating renormalizable gauge theories on the null plane. In order to lay down the groundwork for upcoming nonperturbative studies, it is indispensable to gain control over the perturbative treatment first. A discussion of one-loop renormalization of QED in the Hamiltonian formalism is presented. In this approach, one is faced with severe infrared divergences characteristic of the light-cone gauge. We show how to treat these divergences in a coherent fashion, and thus recover the usual results of the renormalization procedure such as Ward identities and coupling-constant renormalizations.
Relativistic constituent-quark model of nucleon form factors: P. Chung and F. Coester, Phys. Rev. D44, 229 (1991). Abstract We explore the electromagnetic properties of relativistic constituent-quark models of the proton and neutron, in particular their dependence on the constituent-quark mass and the confinement scale. Relativistic effects are never negligible in any model which fits the charge radius of the proton. For a fixed charge radius the confinement scale decreases with decreasing quark masses. Nonvanishing Pauli moments of the constituent quarks are needed to fit the magnetic moments for any value of the quark mass and confinement scale. It is possible to describe existing form-factor data at least up to momentum transfers GeV with quark masses significantly smaller than the conventional nonrelativistic choice of about one-third of the nucleon mass.
Renormalization in the light-front Tamm-Dancoff approach to field theory: R.J. Perry and A. Harindranath, Phys. Rev. D43, 4051 (1991). Abstract It has recently been proposed that light-front field theory provides a powerful tool for the analysis of relativistic bound states when one makes a Tamm-Dancoff truncation. Such a truncation introduces nonlocalities that require an unfamiliar nonlocal renormalization procedure, in which counterterms are allowed to depend on the sectors of Fock space within which or between which they act. In this paper we illustrate the simplest features of the light-front Tamm-Dancoff approach using the Yukawa model in 1+1 dimensions.
Rotational invariance in light-cone quantization: M. Burkardt and A. Langnau, Stanford University preprint, SLAC-PUB-5611. Abstract In the study of the decay of a heavy scalar particle at rest in the Yukawa model at the one and two loop level, it is shown explicitly that naive light-cone quantization leads to a violation of rotational invariance. Noncovariant counterterms are constructed in detail to restore Lorentz covariance. An analysis of surface and zero mode contributions clarifies the origin of the problem.
Testing discretized light-cone quantization: with positronium and heavy quarkonia (I).: M. Krautgärtner, H.C. Pauli, and F. Wölz, MPIH-V4-1991, Max-Planck-Institut für Kernphysik preprint. Abstract A non-pertubative method for solving quantum field theories in three-space one-time dimensions is applied to the bound state problem of positronium and heavy quarkonia. The model includes only one dynamical photon, i.e. the irradiation channels are closed. An integral equation of the Bethe-Salpeter type is derived, being the light-cone analogue of the Tamm-Dancoff equation, and solved numerically. The model accounts for the Bohr-Sommerfield and Dirac physics like the hyperfine splitting including the correct retardation. Numerical results for the mass spectrum and the wave functions are presented, and compared to analytical results. Agreement is found to within the expected accuracy. Special emphasis is put on the role of the Coulomb singularity in momentum space.
The fermionic Schwinger model in light cone quantisation: T. Heinzl, S. Krusche and E. Werner, Universität Regensburg preprint, TPR 91-20, submitted to Phys. Lett. B. Abstract We discuss the light cone approach to the fermionic Schwinger model in the framework of the Dirac-Bergmann algorithm. Quantising via the generalised correspondence principle, which converts Dirac brackets into (anti) commutators and constraints into operator identities, is ambiguous, due to appearing ultraviolet divergencies. To overcome this difficulty, we propose an ultraviolet regularisation of the Dirac-Bergmann algorithm and as a result derive the correct commutator algebra via the generalised correspondence principle. Finally, we suggest how to construct a fermion condensate in this model.
The light cone Feynman rules beyond tree level: A. Bassetto, Invited talk at XIV Workshop ``Problems on High Energy Physics and Field Theory,'' Protvino (USSR) 1991, to appear in the Proceedings. Abstract Light cone Feynman rules are reconsidered in the light of the Mandelstam-Leibbrandt prescription for the spurious singularity in the vector propagator. A procedure is proposed to handle divergences occurring in loop diagrams as well as to renormalize the theory order by order in its loop expansion.
The photon distribution of atoms and molecules: M. Burkardt, Stanford University preprint, SLAC-PUB-5610, August 1991. Abstract In the weak coupling limit of QED, it is shown how to express the parton distribution - in particular the photon distribution - in terms of the nonrelativistic wavefunctions. A sum rule is derived, relating the momentum carried by the photons to the binding energy, thus allowing quantitative predictions about the modification of the photon distribution as molecules are formed from atoms. The physical content is illustrated in a semi-classical picture as well as by providing analytic results for positronium.
Two fermion bound state equation using light front Tamm-Dancoff in 3+1 dimensions: P.M. Wort, Ottawa Carleton Institute for Physics preprint, 12 November 1991. Abstract Attention has recently been paid to Light Front Tamm-Dancoff field theory in 1+1 dimensions, including the proposition of a sector dependent renormalisation procedure. We extend this formalism to 3+1 dimensions, and examine a two fermion system using Light Front field theory in the lowest non-trivial Tamm-Dancoff approximation. It is found that extension to 3+1 dimensions requires some modification of the renormalisation procedure, and we present the bound state equation which results subsequent to this modification.
Zero point energies in light cone field theory: C.J. Benesh and J.P. Vary, Z. Phys. C - Particles and Fields 49, 411 (1991). Abstract In this paper, we study the role of zero point energies in light front quantized field theories using a simple scalar field model with quartic coupling. In the equal time formalism, the zero point energies are renomalized by normal ordering with respect to some vacuum state, which is varied to determine the true, interacting vacuum. On the light front, we shall see that this procedure acquires an unexpected subtlety due to the equivalence of the ultraviolet and infrared limits of the light front momentum. In order for the divergent zero point contributions to and to cancel, we find that the product of the infrared and ultraviolet cutoffs must be a finite constant whose value is determined by the coupling constants of the theory. As an application, we determine the vacuum structure of the theory in two dimensions as a function of the quartic coupling. Finally, we discuss the implications of our result for the discretized versions of light front quantization.
A special example of relativistic hamiltonian field theory: S.D. G azek and R.J. Perry, The Ohio State University preprint, January 22, 1992. Abstract We study fermion-boson bound and scattering states in a 3+1 dimensional Yukawa theory, using a Tamm-Dancoff truncation of light-front field theory. We retain only two sectors of Fock space, the sector with one fermion and the sector with one fermion and one boson. Such truncations violate Lorentz covariance if one employs the canonical Hamiltonian. In order to restore covariance we modify the Hamiltonian, introducing new terms and allowing all terms to depend on the Fock space sectors within which or between which they act. In this special example, which is closely related to the Lee model, simple sector-dependent mass and vertex counterterms are sufficient to yield finite observables that are exactly covariant for states whose invariant mass is less than a critical value determined by the cutoffs. Triviality prevents the complete removal of cutoffs from the Hamiltonian that we consider. This calculation illuminates several basic features of the renormalization program required by the non-perturbative Light-Front Tamm-Dancoff approach.
Asymptotic freedom in Hamiltonian light-front quantum chromodynamics: R. Perry, A. Harindranath and W. Zhang, Ohi State University Preprint, June 11, 1992. Abstract We compute the leading ultraviolet divergent corrections to the quark-gluon vertex in light-front QCD using Hamiltonian perturbation theory, obtaining the running coupling constant familiar from Feynman perturbation theory. Asymptotic freedom arises only after cancellations of severe light-front infrared divergences that are typically avoided in light-cone gauge Feynman formulation, and even if they were to cancel in observables to each order in perturbation theory, we believe they signal important effects in the full theory that cannot be seen using perturbation theory with the naive canonical Hamiltonian.
Basis function calculations for the mass Schwinger model in the light-front Tamm-Dancoff approximation: Y. Mo and R. Perry, Ohio State University Preprint, May 7, 1992. Abstract We use light-front field theory to study the massive Schwinger model. After making a Tamm-Dancoff truncation of Fock space so that no more than four particles are allowed in any state, the coupled light-front Tamm-Dancoff integral equations for charge zero states are solved by expanding the two-particle and four-particle amplitudes in a finite basis, thereby converting the original equations into a simple matrix equation. By retaining the four-particle sector we are able to study both the lowest energy boson of the theory and the first excited state, which for massless fermions is a scattering state of two ground state bosons. Known results for the massless Schwinger model are accurately reproduced with reasonably small bases, and existing numerical results for the massive model are reproduced and improved. The rich physics of the Schwinger model is used to elucidate several simple problems in the use of basis functions to solve Hamiltonian field theories.
Constraints in light-front quantized field theory: P. Srivastava, Ohio State University Preprint 1992. Abstract The quantized theory in the light-front framework of a multiplet of scalar field transforming under a continuous group is constructed following the (standard) Dirac procedure. In the interacting theory the operators satisfy the free field commutation relations only in the continuum limit since the zero modes do not commute with the nonzero ones for finite volume. Interaction dependent non-local operator constraints (absent in the free theory) must be taken care of along with the Hamiltonian. At the tree level they lead to the result that the values of the background field (vacuum expectation values of the field) are obtained from like in the case of quantization at equal-times. For the case of spontaneous symmetry breaking potential a set of these values define an isovector which characterizes a (non-perturbative) vacuum state. The infinite degeneracy of the vacuum is described by the continuum of the allowed orientations of this background isovector in the isospin space. The quantum field theory symmetry generators always annihilate the vacuum in contrast to the case of equal-time quantization. Not all of them are, however, conserved in the quantized theory and the conserved ones determine the surviving symmetry of the quantum theory Lagrangian. The number of Goldstone bosons is the same as in the equal-time case. The constraint also implies that the high order quantum correction will modify the values of the background fields and, for example, the well known instability of the symmetric phase in 1+1 dimensions follows on using the constraint.
Hyperfine splitting in the light-cone Tamm-Dancoff equation of QED and QCD: M. Kaluza and H. Pirner, Universität Heidelberg Preprint, HD-TVP-92-8. Abstract The light-cone Tamm-Dancoff equation reproduces the correct leading order hyperfine splitting (excluding annihilation channel contribution) of the ground state of positronium in QED and the correct leading order hyperfine splittings (excluding annihilation channel contributions) of the ground states of heavy quarkonia in QCD.
Mass renormalization in light-front Tamm Dancoff QED: O. Abe, K. Tanaka and K. Wilson, Ohio State University Preprint, DOE/ER/01545-564. Abstract A discussion of mass renormalization in Light-Front Tamm-Dancoff approximation in QED is presented. The covariant mass counter term, that is, one independent of external momenta and free from infrared cut-off parameter, is obtained for an electron by the use of transverse dimensional regularization method. The result coincides with perturbative result. The mass counter term so obtained enables one to obtain a relativistic equation for bound states. The mass counter terms for a hydrogen atom are also considered. We take the nonrelativistic limit and the S-wave energy levels are obtained.
Nonperturbative light cone quantum field theory beyond the tree level: T. Heinzl, S. Krusche, S. Simbürger and E. Werner, Universität Regensburg, TPR 92-16. Abstract We demonstrate the appearance of spontaneous symmetry breaking induced by nonperturbative quantum corrections for scalar light cone quantum field theory in 1+1 dimensions. We define a light cone effective potential and obtain a second order phase transition.
On the relativistic bound state problem in the light-front Yukawa model: S. G azek, A. Harindranath, S. Pinsky, J. Shigemitsu and K. Wilson, Ohio State University Preprint, OHSTPY-HEP-T-92-004. Abstract We have studied the renormalization problem on the light-front for the 2-fermion bound state in the 3+1 Yukawa model, working within the lowest order Tamm-Dancoff approximation. In addition to traditional mass and wavefunction renormalization, new types of counterterms are required. These are nonlocal and involve arbitary functions of the longitudinal momenta. Their appearance is consistent with general power-counting arguments on the light-front. We have estimated the ``arbitrary function'' in two ways: 1. by using perturbation theory as a guide and 2. by considering the asymptotic large transverse momentum behavior of the kernel in the bound state equations. The latter method, as it is currently implemented, is applicable only to the helicity zero sector of the theory. Due to triviality, in the Yukawa model one must retain a finite cutoff in order to have a nonvanishing renormalized coupling. For the range of renormalized couplings (and cutoffs) allowed by triviality, one finds that the perturbative counterterm does a good job in eliminating cutoff dependence in the low energy spectrum (masses ).
Renormalization of light-cone Tamm-Dancoff integral equation: S. Pinsky, Ohio State University Preprint, OHSTPY-HEP-T-92-006. Abstract Tamm-Dancoff (TD) field theory dates back nearly thirty years, however, this approach to quantum field theory suffered from severe problems related to the formulation of the vacuum energy of the theory. Recently, however, the TD approach has been used in conjunction with light-cone (LC) quantization which has as one of it's great virtues a particularly simple vacuum structure. It is hoped that the combination, LCTD field theory, will become a powerful new technique for solving strongly coupled systems. The state vectors in LCTD field theory are expanded in terms of an infinite set of Fock states which are coupled through an infinite set of coupled eigenvalue integral equations. If we truncate the Fock space however, we find high transverse momentum divergence that do not correspond to any divergence seen in Feynmann perturbation theory. Truncating the Fock space can also break Lorentz covariance. The new renormalization procedure that we propose for LCTD integral equation removes the cutoff dependence in physical quantities, and gives rise to a continuous degree of freedom. In ref. 1 it is shown that this degree of freedom can be used to assure that the bound spectrum has the spacing required by Lorentz covariance. In this talk I will illustrate this new renormalization procedure by considering simple one and two dimensional integral equations.
Solving 3+1 QCD on the transverse lattice using 1+1 conformal field theory: P. Griffin, Nucl. Phys. B372, 270 (1992). Abstract A new transverse lattice model of 3+1 Yangs-Mills theory is constructed by introducing Wess-Zumino terms into the 2-D unitary non-linear sigma model action for link fields on a 2-D lattice. The Wess-Zumino terms permit one to solve the basic non-linear sigma model dynamics of each link, for discrete values of the bare QCD coupling constant, by applying the representation theory of non-Abelian current (Kac-Moody) algebras. This construction eliminates the need to approximate the non-linear sigma model dynamics of each link with a linear sigma model theory, as in previous transverse lattice formulations. The non-perturbative behavior of the non-linear sigma model is preserved by this construction. While the new model is in principle solvable by a combination of conformal field theory, discrete light-cone and lattice gauge theory techniques, it is more realistically suited for study with a Tamm-Dancoff truncation of excited states. In this context, it may serve as a useful framework for the study of non-perturbative phenomena in QCD via analytic techniques.
Spontaneous symmetry breaking mechanism in light-front quantized field theory (discretized formulation): P. Srivastava, Ohio State University Preprint 1992. Abstract Following the ( standard) Dirac procedure, we quantize the scalar field in the light-front framework. The zero mode operator is shown to commute with the nonzero ones only in the continuum limit. In the interacting theory we are left with a non-local constraint along with the Hamiltonian. At the tree level it leads to the result that the values of the background field are obtained from like in the case of quantization at equal-times. For the case of spontaneous symmetry breaking potential these values characterize the various (non-perturbative) vacua. The corresponding Fock spaces are built by applying the nonzero mode operators to the vacuum. In the renormalized theory the constraint leads to the well known result on the instability of the symmetric phase for large enough coupling constant in 1+1 dimensions.
Staggered fermions and chiral symmetry breaking in transverse lattice regulated QED: P. Griffin, University of Florida, UFIFT-HEP-92-19. Abstract Staggered fermions are constructed for the transverse lattice regularization scheme. The weak perturbation theory of transverse lattice non-compact QED is developed in light-cone gauge, and we argue that for fixed lattice spacing this theory is ultraviolet finite, order by order in perturbation theory. However, by calculating the anomalous scaling dimension of the link fields, we find that the interaction Hamiltonian becomes non-renormalizable for , where g(a) is the bare (lattice) QED coupling constant. We conjecture that this is the critical point of the chiral symmetry breaking phase transition in QED. Non-perturbative chiral symmetry breaking is then studied in the strong coupling limit. The discrete remnant of chiral symmetry that remains on the lattice is spontaneously broken, and the ground state to lowest order in the strong coupling expansion corresponds to the classical ground state of the two-dimensional spin one-half Heisenberg antiferromagnet.
The challenge of light-cone quantization of gauge field theory: S. Brodsky, G. McCartor, H. Pauli and S. Pinsky, Ohio State University preprint, OHSTPY-HEP-T-92-005.
The sine-Gordon model and the small region of light-cone perturbation theory: P. Griffin, University of Florida, UFIFT-HEP-92-17. Abstract The non-perturbative ultraviolet divergence of the sine-Gordon model is used to study the region of light-cone perturbation theory. The light-cone vacuum is shown to be unstable at the non-perturbative critical point by a light-cone version of Coleman's variational method. Vacuum bubbles, which are diagrams in light-cone field theory and are individually finite and non-vanishing for all , conspire to generate ultraviolet divergences of the light-cone energy density. The region of momentum also contributes to connected Green's functions; the connected two point function will not diverge, as it should, at the critical point unless diagrams which contribute only at are properly included. This analysis shows in a simple way how the region cannot be ignored even for connected diagrams. This phenomenon is expected to occur in higher dimensional gauge theories starting at two loop order in light-cone perturbation theory.
Ultraviolet regularization of light-cone Hamiltonian perturbation theory: application to the anomalous magnetic moment of the electron (g-2) in light-cone gauge: A. Langnau and M. Burkardt, SLAC Preprint, SLAC-PUB-5668, May 1992. Abstract An ultraviolet regularization and renormalization procedure of light-cone perturbation theory, which is suitable for a numerical application is discussed. The fourth order correction to the anomalous magnetic moment of the electron in the light-cone gauge is computed. Several regularizations of the associated light-cone gauge singularity are explored. Local counterterms are constructed to remove the quadratic light-cone divergences from the formalism. Problems of the Discrete Light-Cone Quantization (DLCQ), beyond the one photon exchange, are also described.