50 Years of Yang-Mills Theory

There’s a new book out, entitled 50 Years of Yang-Mills Theory, edited by Gerard ‘t Hooft. It contains some excellent review articles about topics related to Yang-Mills theory, together with short introductions by ‘t Hooft. Many but not all of the articles have already appeared at the arXiv as preprints.

The book begins with an article by deWitt, unfortunately unfinished at the time of his death, about the space of gauge fields. ‘t Hooft’s introduction and deWitt’s historical comments makes clear that “Fadeev-Popov” ghosts really should also have deWitt’s name attached to them. The full Faddeev-Popov paper is included in the book, a good idea since I don’t think it was ever published. It appeared in Russian as a Kiev preprint in 1967, was translated into English and appeared as a preprint in 1972. While looking for information about this paper on the web, I noticed that Fermilab has put up scanned versions of their preprints, which is useful for the ones from the seventies and eighties that predate the arXiv.

There’s an excellent review of the “Higgs mechanism” by Englert, where again Englert’s name deserves equal time with that of Higgs. This paper has appeared as a preprint. Steven Weinberg contributes an interesting review article about the making of the standard model and his role in it. There are three articles related to renormalization of Yang-Mills: a detailed one by the master himself (‘t Hooft), a mystifying one about Koszul complexes by Raymond Stora, and one about Slavnov-Taylor identities by Carlo Becchi.

Steve Adler has a long article about the history of what is now known as the “Adler-Bell-Jackiw” anomaly, and Jackiw has one about various topics related to Yang-Mills theory that he has contributed to, including anomalies, Chern-Simon terms, and gravitation. There’s also an article by Frank Wilczek, mainly about asymptotic freedom, and one by Alexander Bais about magnetic monopoles in Yang-Mills theory.

On the non-perturbative side of things, there is Alexander Polyakov writing about string theory and confinement (he thinks string theory needs to have its head examined, see an earlier posting here). Pierre van Baal contributes a very interesting article on “Non-perturbative Aspects of Gauge Fixing”, Michael Creutz a mainly historical article about lattice gauge theory. Peter Hasenfratz writes about chiral symmetry on the lattice. Both he and Creutz note that, while progress has been made, handling chiral gauge theories on the lattice remains somewhat problematic, so there is still no really satisfactory non-perturbative version of the electroweak part of the standard model.

Alvaro de Rujula has an entertaining discussion of events surrounding the “November Revolution” in 1974. Finally, there’s a review article about supergravity by Peter van Nieuwenhuizen, and one by Witten reviewing the twistor space formulation of perturbative Yang-Mills amplitudes. Witten’s article doesn’t seem to have appeared on the arXiv (although there is a new review article by Cachazo and Svrcek which covers this material and much more).

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7 Responses to 50 Years of Yang-Mills Theory

  1. Anonymous says:

    noninteracting spin-2 isn’t gravity either

  2. Anonymous says:

    massive spin-2 isn’t gravity

  3. D R Lunsford says:

    To me, spin 2 connotes a background.


  4. JC says:


    What’s a good counterexample, where spin 2 is NOT gravity?

  5. D R Lunsford says:

    Weinberg has the best line for years – “radial and azimuthal physicists” – ROFL!

    I was somewhat confused by the SG review. Apparently everyone just assumes spin 2 “is” gravity.


  6. Anonymous says:

    Off-topic, but I thought I should mention it: The BBC’s “The Changing World” (broadcast here by PRI) is doing an hour tonight on the effects of visa restrictions on foreign researchers in the U.S.

    In the same vein see Sean Carroll’s recent post.

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