Polyakov remembers the development of Renormalization Group and Conformal Bootstrap as "With the use of the ingenious technique, developed by Gribov and Migdal [1] in the problem of reggeons, I found connections between phenomenological theory and “bootstrap” equations (Polyakov [2]). Sasha Migdal did very similar work independently. There was also something new–I formulated “fusion rules” for correlations, which we now would call operator product expansion [3]. I had mixed feelings when I found out later that the same rules at the same time and in more generality have been found by L. Kadanoff [4] and K. Wilson [5].

While for the Renormalization Group, we frequently also mentioned the names of K. Wilson and Michael Fisher together (e.g. Wilson-Fisher fixed point).

question: What roles had Gribov, Migdal, Polyakov, L. Kadanoff, K. Wilson and M. Fisher play in the Renormalization Group?

P.S. It seems that K. Wilson gets the most credit for the development of Renormalization Group (a single recipient for Nobel Prize in Physics (1982)). But M. Fisher, L. Kadanoff and K. Wilson share credits for the earlier Wolf Prize in Physics (1980), for "for pathbreaking developments culminating in the general theory of the critical behavior at transitions between the different thermodynamic phases of matter."

A side question: Why does K Wilson get the most credits for this subject?


[1] V. Gribov and A. Migdal, ZHETF 55, 1498 (1968).

[2] A. Polyakov, ZHETF 55, 1026 (1968)

[3] A. Polyakov, ZHETF 57, 271 (1969).

[4] L. Kadanoff, Phys. Rev. Lett. 23, 1430 (1969).

[5] K. Wilson, Phys. Rev. 179, 1499 (1969).

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    $\begingroup$ Post discussed in the hbar chat room here. $\endgroup$
    – Qmechanic
    Commented Jan 4, 2017 at 14:54
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    $\begingroup$ I'm voting to close this question as off-topic because it is about history instead of physics. $\endgroup$ Commented Jan 4, 2017 at 15:14
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    $\begingroup$ This is history of a rather technical topic in physics, the OPE, and as such it should be more of interest to physicists than historians. Closing or migration to hsm SE is a not so subtle form of censorship. $\endgroup$
    – Abdelmalek Abdesselam
    Commented Jan 4, 2017 at 15:44
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    $\begingroup$ @AccidentalFourierTransform: I guess there is no use arguing with the thought police. $\endgroup$ Commented Jan 4, 2017 at 20:38
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    $\begingroup$ The burden of proof so to speak is on you since YOU wanted the question migrated. I asked YOU to provide a reason why the question had no place on physicsSE and you didn't give any. I find your last comment very condescending and arrogant. You really think I need a lecture on the difference between expressing dissatisfaction and presenting arguments for a case. $\endgroup$ Commented Jan 4, 2017 at 21:02

1 Answer 1


I think the quote (a reference would be good) is more about the OPE than the RG although they are very closely related and must have germinated in Wilson's mind concurrently. About Wilson's priority regarding the OPE, the correct date for his paper is 1964 rather than 1969 which seems to make his contribution posterior to that of the Soviet School. They didn't have arXiv at the time and Wilson's Cornell preprint did not get a wide circulation (perhaps also because it had a mistake regarding anomalous dimensions). See section 1.11 of this article for more references and in particular a 1967 Ann. Phys. paper by Brandt with an account of Wilson's OPE.

Edit: Regarding Wilson's error about anomalous dimensions in the original OPE preprint, see Section 4 of this recent article by Peskin dedicated to Wilson's work.

  • $\begingroup$ Thanks for the nice answer, the quote is from Polyakov's own view: arxiv.org/abs/hep-th/9211140. I am trying to read these papers to get better ideas why Wilson's framework is the highest and the renowned. $\endgroup$
    – wonderich
    Commented Jan 4, 2017 at 21:44
  • $\begingroup$ @wonderich: Thanks! I edited the answer with a link to Brandt's paper which, as far as I know is the first published account of Wilson's OPE. $\endgroup$ Commented Jan 4, 2017 at 21:51
  • $\begingroup$ In my opinion: A simple answer for Wilson's role may be that he is the best person to see through RG in the eyes of statistical physics as well as particle physics. $\endgroup$
    – wonderich
    Commented Jan 4, 2017 at 22:11
  • $\begingroup$ Well... I don't know since this goes into subjective terrain. If you want the facts, e.g. pointers to early references on the OPE, see Section 1.11 of my article which also mentions the early works by Heisenberg, Euler, Dirac and Valatin. Regarding the broader subject of RG instead of the more specialized OPE, the article by Peskin (and perhaps the whole issue of JSP where it appeared) is very good at explaining the genesis of this set of ideas. $\endgroup$ Commented Jan 4, 2017 at 22:20

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