Why Renormalization Group is a Fun Thing

With the hope that this will motivate someone to read these original articles, we quote some famous words on Renormalization Group (RG) in chronological order:

K.G. Wilson and J. Kogut, in The Renormalization Group and the epsilon expansion , Physics Reports 12, 75 (1974).

"There has been sensational progress in calculating QED, but very little progress in understanding it; and strong interactions are neither calculable nor understood."

"The early work on the RG had two defects. It had no calculable experimental consequences, so no one had to take it seriously. Secondly, the intuitive ideas were encased in a thick shell of formalism; it has required many years to peal off the shell."

" In place of consciously reducing the number of degrees of freedom, these authors substitute a prayer that an infinite sum of graphs can be replaced by a calculable subset."

K.G. Wilson, in The Renormalization Group: Critical Phenomena and the Kondo problem , Reviews of Modern Physics, 47, 773 (1975).

" ... original Gell-Mann-Low RG theory and the Callan-Symanzik equations ... They are efficient calculational methods (for Feynman diagrams). ... They completely hide the physics of many scales. These methods are hard to follow in detail for physicists without quantum field theoretical training. "

K. G. Wilson, in Renormalization Group Methods, in Advances in Mathematics, 16, 170 (1975).
"It (RG) is at present an approach of last resort, to be used only when all other approaches have been tried and discarded. The reason for this is that it is rather difficult to formulate RG methods for new problems; in fact the RG approach generally seems as hopeless as any other approach until someone succeeds in solving the problem by RG approach."

K.G. Wilson, in Renormalization Group and Critical Phenomena, Reviews of Modern Physics, 55, 583 (1983).
" There are many reparametrizations of QED that eliminate the divergences but use different finite quantities than e and m to replace e_0 and m_0. Stueckelberg and Petermann observed that the transformation groups could be defined which relate different reparametrizations. They called these groups "groupes de normalization", which is translated "renormalization groups"."

S. Weinberg, in Why the Renormalization Group is a Good Thing in "Asymptotic Realms of Physics", Essays in honor of Francis Low, edited by A. Guth, K. Huang and R.L. Jaffe, the MIT Press, Cambridge, Massachusetts (1983).
" ... I say this with some bitterness because I remember around 1960 when that book (Bogoliubov and Shirkov) came out thinking that the RG was pretty hot stuff, and trying to understand it and finding it just incomprehensible and putting it away. I made the mistake of not going back and reading carefully the paper by Gell-Mann and Low, which is quite clear and explains it all well. (Incidentally, the later text book by Bjorken and Drell gave a good clear explanation of all this, following the spirit of the Gell-Mann-Low paper)."

A. Zee, in It is not dangerous, subheading of "Renormalization Group flow as a natural concept in High Energy Physics and Condensed Matter", chapter VI.8 of "Quantum Theory in a Nutshell", Princeton University Press (2003).
Begins with the quote "Therefore conclusions based on the RG arguments ... are dangerous and must be viewed with due caution. So is it with all conclusions from local relativistic field theories" -- Bjorken and Drell, Vol. II.
and continues
"The discussions in some of the older books are downright misleading and confused, such as the well-known text from which I learned quantum field theory and from which the quote above is taken."

Compiled on December 19, 2003 by a.h