I wanted to know if the discussion on Wilson loops and Polyakov loops (and their relationship to confinement and asymptotic freedom) is present in the three volumes of Weinberg's QFT books but in some other name or heading.

At least I couldn't naively find these topics in that book.

I was hoping to see some detailed discussion about these non-local physical observables and also may be some model calculations and evaluations of them in some gauge theories. In Eduardo Fradkin's lecture notes there exists an evaluation of the Wilson loop in free Maxwell's theory and that too in a certain limit of large time and large separation and thats the only example of such a calculation that I have seen.

(Aside: I would be grateful if people can also point to other pedagogic/classic/path-breaking papers/references in this topic of Wilson loops. To start off these are four papers that I came across while searching along this direction: arXiv:hep-th/0003055, arXiv:hep-th/9911088, arXiv:0905.2317, arXiv:hep-th/9803002.)


The original papers by Gerard 't Hooft himself are quite readable.

Whenever I open these papers, I'm always awestruck.

  • $\begingroup$ Thanks a lot for the references! You have any insights about whether Weinberg has somehow garbed this topic of Wilson/Polyakov loops in some other form/terminology? It would be weird if this classic topic in gauge theory doesn't feature in the classic book on QFT! $\endgroup$ – user6818 Dec 28 '11 at 22:54
  • $\begingroup$ I don't know if it's in it or not (look for "area law" or "confinement" in it). Note that you and I may think this topic as classic, but I guess it can be too modern a topic for him. Anyway, just stop regarding his book as sacred. $\endgroup$ – Yuji Dec 29 '11 at 0:56
  • $\begingroup$ Thanks! It does seem that more and more I try to get into string theory research I am actually reading less and less of the 3 volumes of Weinberg! (...of course I am trying to read more of Polchinski's volume 2 now which seems largely disconnected from his volume 1...) But clearly there would have been a lot of mental peace and ease had I known everything in the 3 volumes by Weinberg before I started on Polchinski. Kind of feel "guilty" that I couldn't do so! $\endgroup$ – user6818 Jul 6 '12 at 20:04

The lecture 7 and 10 by Witten in the following book contain a good review on this issue.

Quantum fields and strings: a course for mathematicians, Volume 2

  • $\begingroup$ @Satoshi Thanks for the link! I did look through that. $\endgroup$ – user6818 Jul 6 '12 at 20:04

Your Answer

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.