Anderson on Anderson-Higgs

Philip Anderson was here at Columbia yesterday, and gave a very interesting talk, mostly discussing what was going on in the late 50s and early 60s at the intersection of condensed matter and particle physics. This has attracted a lot of interest around the question of who first came up with what is now called the “Higgs mechanism” and who first predicted a “Higgs particle” (I’ve written a long blog posting about this here).

After the discovery of the BCS model of superconductivity, Anderson did important work on understanding the “gauge problem” of how gauge symmetry acts in such a theory, publishing a series of papers on this in 1958. He joked that he was “pretty naive about field theory” at the time, so much so that the spelling he was using was “guage”. He had the advantage of regularly talking with Bardeen and with Nambu, and he described some of Nambu’s work on the so-called “Nambu-Jona-Lasinio” model. His 1958 work explained how one avoids getting massless Goldstone bosons in superconductors due to the singular long range nature of the Coulomb force. His talk included an anecdote about escaping from handlers in the Soviet Union to get a chance to explain this to Shirkov during a visit there (he wasn’t allowed to meet Bogoliubov).

He was at Bell Labs in the summer of 1962, and talked to J.G. Taylor, who told him that the problem of massless Goldstones was something those in particle theory were actively worrying about. Taylor also gave him a copy of Schwinger’s Gauge invariance and mass paper, which had been published that January. This led to Anderson’s Plasmons, gauge invariance, and mass paper, finished in November, and published in April 1963. This paper clearly explains the nature of what is now generally referred to as the “Higgs mechanism”, in the Yang-Mills case, not just the Abelian case, ending with the very modern point of view

We conclude, then, that the Goldstone zero-mass difficulty is not a serious one, because we can probably cancel it off against an equal Yang-Mills zero-mass problem.

In 1964 the papers by Brout-Englert-Higgs-Guralnick-Hagen-Kibble appeared that have drawn the most attention as earliest instances of the Higgs mechanism, but Anderson had the correct idea a couple years earlier. He described the situation as one where he and the 1964 authors all had the right explanation for why the W and Z have mass, although none of them (including him) had the actual physical Higgs particle, which he claimed first appears in a 1966 paper of Higgs.

The main point of his talk was the fruitful nature of research at the intersection between problems in condensed matter and particle theory, with the 50s-60s a happy period of such work. He ended with some comments on “supersolids”, see his recent paper about this here. Anderson will be 90 years old later this year (he’s almost exactly the same age as Freeman Dyson) and it was great to see him still going strong.

Update: See here for a write-up by Anderson of a talk a few years ago covering much the same material as yesterday’s Columbia talk (including the story of meeting Shirkov).

Update: A commenter points to this recent talk by Guralnik at Brown and mentions some comments that might be about Frank Close.

I just watched the talk, and he explicitly refers to this exchange in the London Times. I don’t see how when he says

the person involved as far as we can tell has no understanding whatsoever of mass renormalization and how these things work.

this can refer to anyone except Close (about whom it is completely absurd). The point of contention here is a very simple one. Guralnik’s paper (unlike Higgs’s) has no potential term for the scalar field. In his talk he says this is because it was the practice at Harvard not to write such terms down, while knowing they had to appear to renormalize the theory. Close’s point I think is just that Higgs went further than the other authors at the time in terms of exhibiting what would be needed to study the dynamics of the physical mode of the scalar field. From what I can tell, of course everyone writing these papers knew about potential terms for the scalar and how they worked, but the whole issue is a bit irrelevant: none of the people involved at this period seem to have thought seriously about this physical mode that describes the Higgs particle itself. They were thinking about something entirely different, the mass of the gauge field, and in any case these are Abelian models that have nothing to do with the real non-Abelian model that describes the Higgs particle.

The main point of Guralnik’s talk as far as this controversy goes I think is his explicit and repeated claim (which seems to me debatable) that Higgs’s paper was just wrong for technical reasons, in the sense of reaching correct conclusions by an incorrect argument. This appears to be Guralnik’s argument for why he and his collaborators should be preferred to Higgs as candidates for a Nobel, and is made much more strongly here than in other places (such as here, where he doesn’t use the term “wrong”, emphasizes more why Higgs’s argument was “incomplete”).

Leon Cooper was in the audience, and asks Guralnik about the Anderson explanation for why the Goldstone theorem is violated here: the long range nature of the Coulomb potential. Guralnik seems to acknowledge that this is the right physical way to understand what is going on, but says that relativity makes things more complicated. He explicitly acknowledges that he understood not at all Anderson’s arguments, saying

we were woefully ignorant, had barely heard of superconductivity.

About the crucial question of priority, the fact that his competitor’s papers were published earlier, were read by him before submission of his paper, and explicitly referenced in his paper, all he says is

as we published it, we found out about other papers.

which really doesn’t do justice to the situation. In this piece, written after the Higgs discovery, he describes the history as

We finally submitted our paper to PRL with the proof of the general mechanism to avoid the Nambu Goldstone theorem (the only work to have this) and the special example. We were surprised to discover that two very different but related papers, with parts of the example, one by Englert and Brout and the other by Higgs also existed. All three papers appeared in the same volume of PRL in 1964.

which is highly misleading.