This is the part 2 following the part 1 question.

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 mentioned the names of Gribov, Migdal, Polyakov, L. Kadanoff, K. Wilson and M. Fisher, it seems that Polyakov gets the most credit for the development of Conformal Bootstrap.

But in the early 1970s, at least three groups of people working on CFTs. The Italy group of Raoul Gatto collaborated with Sergio Ferrara, Aurelio Grillo and Giorgio Parisi. In Germany, there were Gerhard Mack and Martin L¨uscher. In Russia, Alexander Polyakov and Alexander Migdal. The three original papers on conformal bootstrap came from these groups: Ferrara, Grillo, and Gatto [6], Polyakov [7], and Mack [8].

question: What are the roles of Ferrara, Grillo, Parisi; Gatto; Mack, L¨uscher; Polyakov and Migdal? Why does A Polyakov get the most credits for the conformal bootstrap, but not the Renormalization Group?


[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).

[6] S. Ferrara, A. F. Grillo, and R. Gatto, “Tensor representations of conformal algebra and conformally covariant operator product expansion,” Annals Phys. 76 (1973) 161–188.

[7] A. M. Polyakov, “Nonhamiltonian approach to conformal quantum field theory,” Zh. Eksp. Teor. Fiz. 66 (1974) 23–42.

[8] G. Mack, “Duality in quantum field theory,” Nucl. Phys. B118 (1977) 445–457

  • $\begingroup$ This seems to be a question about the history (or sociology?) of physics, rather than the concepts of physics. Perhaps History of Science and Mathematics SE would be more appropriate? $\endgroup$ – sammy gerbil Dec 22 '16 at 9:30
  • $\begingroup$ @sammy gerbil, do you think that people in History of Science and Mathematics SE can answer this techinical questions? ---one needs to understand the cited papers and their physics well enough to judge their work. I doubt any of us in Physics SE can answer it... $\endgroup$ – user32229 Dec 23 '16 at 3:03
  • $\begingroup$ @mysteriousness : Assessing why one person rather than another gets credit is a question of sociology or history (or even politics). It depends on personal or historical factors. It cannot be answered using physical principles. A historian or sociologist would have a better chance of answering, if such a question can be answered. Otherwise, without citation of historical evidence, the only answers which can be given here are opinions, and a question which merely asks for opinions is off topic. Physics does not have any way of evaluating personal contributions to science. $\endgroup$ – sammy gerbil Dec 23 '16 at 5:10

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.