Collaborators:
Rajen Kundu
Asmita Mukherjee
Dipankar Chakrabarti
Lubomir Martinovic
James P. Vary
Since Discrete Light Cone Quantization (DLCQ) is a convenient tool to handle longitudinal direction in light front formulation of field theories, it is worthwhile to investigate the merits of DLCQ in the study of non-perturbative aspects of two dimensional field theories. DLCQ also finds applications in string theory/M theory.
From time to time, questions arise in the literature regarding many aspects of DLCQ. We addressed [1] issues related with microcausality violation and continuum limit in the context of (1+1) dimensional scalar field theory in DLCQ in parallel with discretized equal time quantization (DETQ) and the fact that Lorentz invariance and microcausality are restored if one can take the continuum limit properly was emphasized. In the free case, it was shown with numerical evidence that the continuum results can be reproduced from DLCQ results for the Pauli-Jordan function and the real part of Feynman propagator. The contributions coming from $k^+$ near zero region in these cases were found to be very small in contrast to the common belief that $k^+=0$ is an accumulation point. In the interacting case, aspects related to the continuum limit of DLCQ results in perturbation theory were discussed.
Later we addressed [2] problems associated with compactification near and on the light front. These problems were originally posed in the context of some studies in string/M theory. In perturbative scalar field theory we illustrated and clarified the relationships among three approaches: (1) quantization on a space-like surface close to a light front; (2) infinite momentum frame calculations; and (3) quantization on the light front. Our examples emphasized the difference between zero modes in space-like quantization and those in light front quantization. In particular, in perturbative calculations of scalar field theory using discretized light cone quantization there are well-known `zero-mode induced'' interaction terms. However, we showed that they decouple in the continuum limit and covariant answers are reproduced. Thus we showed that the compactification of a light-like surface is feasible and defines a consistent field theory.
To further elaborate on this issue, we studied [3] the S-matrix of two-dimensional phi4 theory in DLCQ and showed how the correct continuum limit is reached for various processes in lowest order perturbation theory.
A persistent question regarding DLCQ was its ability to address issues concerning spontaneous symmetry breaking and topological structures in field theory. Following some initial work of Rozowsky and Thorn, we investigated [4] non-trivial topological structures in DLCQ through the example of the broken symmetry phase of the two dimensional phi4 theory using anti periodic boundary condition (APBC). We presented evidence for degenerate ground states which is both a signature of spontaneous symmetry breaking and mandatory for the existence of kinks. Guided by a constrained variational calculation with a coherent state ansatz, we then extracted the vacuum energy and kink mass and compare with classical and semi - classical results. We compared the DLCQ results for the number density of bosons in the kink state and the Fourier transform of the form factor of the kink with corresponding observables in the coherent variational kink state. We consider these results as establishing the viability of DLCQ for addressing non-trivial phenomena in quantum field theory. Similar studies were carried out [5] using periodic boundary condition also. The calculations using APBC were performed also in the strong coupling region [6] to investigate deviations from classical or semiclassical behaviours. Using discrete light cone quantization (DLCQ), we extracted the masses of the lowest few excitations and observe level crossings. To understand this phenomena, we evaluated the expectation value of the integral of the normal ordered phi2 operator and we extracted the number density of constituents in these states. A coherent state variational calculation confirmed that the number density for low-lying states above the transition coupling is dominantly that of a kink-antikink-kink state. The Fourier transform of the form factor of the lowest excitation was extracted which reveals a structure close to a kink-antikink-kink profile. Thus, we demonstrated that the structure of the lowest excitations becomes that of a kink-antikink-kink configuration at moderately strong coupling. We extracted the critical coupling for the transition of the lowest state from that of a kink to a kink-antikink-kink. We interpreted the transition as evidence for the onset of kink condensation which is believed to be the physical mechanism for the symmetry restoring phase transition in two-dimensional phi4 theory.
[1] A Numerical Experiment in DLCQ: Microcausality, Continuum Limit and all
that , Dipankar Chakrabarti, Asmita Mukherjee, Rajen Kundu, and A.
Harindranath, Phys. Lett. B 480, 409 (2000).
[2] Compactification near and on the Light Front, A. Harindranath, L.
Martinovic, and J.P. Vary, Phys. Rev. D 62, 105015 (2000).
[3] Perturbative S-matrix in Discretized Light Cone Quantization of
two-dimensional phi^4 theory, A. Harindranath, L. Martinovic and J.P. Vary,
Phys. Lett. B 536, 250 (2002).
[4] Kinks in Discrete Light Cone Quantization,
Dipankar Chakrabarti, A.
Harindranath, Lubomir Martinovic and James P. Vary,
Phys. Lett. B 582,
196 (2004).
[5] Ab Initio Results for the Broken Phase of Scalar Light Front Field
Theory, Dipankar Chakrabarti, A. Harindranath, Lubomir Martinovic, Grigorii
B. Pivovarov and James P. Vary, Phys. Lett. B 617, 92 (2005).
[6] Transition in the Spectrum of the Topological Sector of
phi42 Theory at
Strong Coupling , Dipankar Chakrabarti, A. Harindranath and James P. Vary,
Phys. Rev. D 71, 125012 (2005).