I have been trying to truly understand the renormalizability of quantum (i.e., without anomalies) gauge theories (after which I will focus on the case with spontaneous symmetry breaking).

The problem is that I have not found any self-contained specific text on the subject. There are, of course, good books which approach it, Weinberg and Itzykson-Zuber, for instance. But since (as far as I have seen) there is no way to scape the BRST formalism, looking at it through these books is having to cover a too large portion of it to understand the notation, conventions and arguments.

In any case, can you indicate what you think to be the best (and more friendly) text (may be book, lecture notes or anything) to formally understand 'the renormalizability of gauge theories'?


1 Answer 1


Depends what you call a "proof" and the level of mathematical rigor you want. If you want mathematically rigorous proofs of renormalizability in the sense of formal power series (perturbative renormalizability) for gauge theories, with BV formalism but no spontaneous symmetry breaking, then I would recommend the book by Kevin Costello "Renormalization and Effective Field Theory". For the spontaneously broken symmetry case, I don't think a book exists. You can try the paper by Kopper and Muller "Renormalization of spontaneously broken $SU(2)$ Yang–Mills theory with flow equations".

  • $\begingroup$ Thank you very much! I have taken a look and the book seems to be a liiittle bit too mathematically invested for what I'm looking for. $\endgroup$
    – GaloisFan
    Jun 14, 2019 at 16:34
  • 2
    $\begingroup$ I thought a fan of Galois wouldn't mind too much math :) $\endgroup$ Jun 14, 2019 at 19:17
  • $\begingroup$ xD The problem is taking the time needed to properly understand axiomatic field theory. $\endgroup$
    – GaloisFan
    Jun 16, 2019 at 0:37
  • $\begingroup$ You are mistaken in thinking you need axiomatic field theory to read any of this. These two references directly go to the heart of the matter about showing convergence or renormalized perturbation theory. $\endgroup$ Jun 16, 2019 at 16:15
  • $\begingroup$ I read the first 15 pages and (admitedly) guessed that was axiomatic field theory. Well, I will try to go through the book's proof, then! Thank you! $\endgroup$
    – GaloisFan
    Jun 19, 2019 at 0:08

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