One reason for this posting is that exchanges in the comment section of the previous one led me to look into some history, and I found some odd and possibly interesting facts I hadn’t previously known. So, part of this will just be lifting of some links from comments in the last posting.
Another reason is that while the history may seem obscure, what’s at issue is the central unsolved problem of particle physics: the nature of electroweak symmetry breaking, and no excuse for thinking more about this topic should be let to pass by. The Yang and Mills work on non-abelian gauge theory published in 1954 had one huge problem: in perturbation theory it has massless particles which don’t correspond to anything we see. One way of getting rid of this problem is now fairly well-understood, the phenomenon of confinement realized in QCD, where the strong interactions get rid of the massless “gluon” states at long distances (they are relevant at short distances, visible in terms of jets seen at colliders).
By the very early sixties, people had begun to understand another source of massless particles: spontaneous symmetry breaking of a continuous symmetry. If the vacuum state is non-invariant under a continuous symmetry, you expect to find one massless state in the theory for each generator of the symmetry. These are called “Nambu-Goldstone” particles, and pions provide an example (only approximately massless, since the symmetry is approximate).
What Philip Anderson realized and worked out in the summer of 1962 was that, when you have both gauge symmetry and spontaneous symmetry breaking, the Nambu-Goldstone massless mode can combine with the massless gauge field modes to produce a physical massive vector field. This is what happens in superconductivity, a subject about which Anderson was (and is) one of the leading experts. His paper on the subject was submitted to Physical Review that November, and appeared in the April 1963 issue of the journal, in the particle physics section. It explains what is commonly called the “Higgs mechanism” in very much the same terms that the subject appears in modern particle physics textbooks and notes:
It is likely, then, considering the superconducting analog, that the way is now open for a degenerate-vacuum theory of the Nambu type without any difficulties involving either zero-mass Yang-Mills gauge bosons or zero-mass Goldstone bosons. These two types of bosons seem capable of “canceling each other out” and leaving finite mass bosons only.
All that is missing here is an explicit relativistic example to supplement the non-relativistic superconductivity one. This was provided by several authors in 1964, with Higgs giving the first explicit relativistic model. Higgs seems also to have been the first to explicitly discuss the existence in models like his of a massive mode, of the sort that we now call a “Higgs particle”, the target of active searches at the Tevatron and LHC.
Anderson tells his story here:
So it was probably completed summer ’62. Very little attention was paid to it except that in fact— well, Higgs reinvented it. In some ways the particle physicists tell me he had less understanding; in some ways he had more. He certainly made a real model out of it where I had only a mechanism…
about the Anderson-Higgs phenomenon, if I may use the word. In the paper that I wrote I definitely said people have been worried about the Goldstone boson in broken symmetry phenomena. The Goldstone boson is not necessary. Here is the possibility of removing the Goldstone boson, mixing it with a gauge boson, and ending up with zero mass. [should be “non-zero” maybe a transcription error]…So I think I really understood the nature of the mechanism…
It was not published as a paper in the Condensed Matter Physics. It was published as a paper in Particle Physics. Brout paid attention to it. And he and Englert two years later produced a model of symmetry breaking, which if you’ll read carefully the summary of their work that t’Hooft and Veltman give (Nobel Prize winner this year), they say that they took off very much from the Brout-Englert paper, and there’s no way Brout was not perfectly aware of my work and I would be surprised if the Brout Englert paper doesn’t reference it rather than Higgs or along with Higgs. So in fact it didn’t fall completely on deaf ears.
Note added 5/15/2013: I’ve heard from Martin Veltman that at the time they were working on the renormalizability of Yang-Mills, he and ’t Hooft were not aware of the Brout/Englert work, or of the general issues about the Goldstone theorem and the Higgs mechanism that Brout/Englert and others were addressing. Veltman’s Nobel lecture describes the history in detail, and has nothing like what Anderson describes (neither does ’t Hooft’s).
Given the background Brout had in condensed matter physics and Anderson’s claim that “there’s no way Brout was not perfectly aware of my work”, it is quite surprising that no reference to Anderson occurs in the paper he and Englert published in Physical Review Letters. It arrived at the journal June 26, 1964 and came out in an issue dated August 31, 1964. In historical talks about this given back in 1997 (available here), Brout and Englert write:
We knew from our study of ferromagnetism that long range forces give mass to the spin waves and we were aware, from Anderson’s analysis of superconductivity [5], of the fact that the massless mode of neutral superconductors, which is also a Nambu-Goldstone mode, disappears in charged superconductors in favor of the usual massive plasma oscillations resulting from the long range coulomb interactions in metals. Comforted by these facts, we decided to confront, in relativistic field theory, the long range forces of Yang-Mills gauge fields with the Nambu-Goldstone bosons of a broken symmetry.
The latter arose from the breaking of a global symmetry and Yang-Mills theory extends the symmetry to a local one [6]. Although the problem in this case is more subtle because of gauge invariance, the emergence of the Nambu-Goldstone massless boson is very similar. We indeed found that there were well defined gauges in which the broken symmetry induces such modes. But, as we expected, the long range forces of the Yang-Mills fields were conflicting with those of the massless Nambu Goldstone fields. The conflict is resolved by the generation of a mass reducing long range forces to short range ones. In addition, gauge invariance requires the Nambu-Goldstone mode to combine with the Yang Mills excitations. In this way, the gauge fields acquire a gauge invariant mass!
This work was finalized in 1964.
Very oddly, the only reference to Anderson’s work that they give (their [5]) is to a 1958 paper of his, not to the 1963 paper which had the same conclusions as theirs, a year earlier.
Brout and Englert don’t give a full model, just assume existence of a scalar field with spontaneously broken symmetry, and specified couplings to the gauge fields. Working independently, Peter Higgs in July 1964 sent a paper to Physics Letters arguing that, even relativistically, Anderson’s argument worked and there is no need for massless particles in the case of spontaneous symmetry breaking with a local symmetry. This paper was published, but a paper he sent a week later in which he wrote down an explicit model (the Abelian Higgs model) was rejected. It was later submitted to (August 31, 1964) and accepted at Physical Review Letters (published in the October 19, 1964 issue), where the referee (Nambu) made Higgs aware of the Brout-Englert paper, which Higgs refers to in a footnote. The Higgs paper does refer to Anderson’s 1963 paper, writing in the introduction:
This phenomenon is just the relativistic analog of the plasmon phenomenon to which Anderson [3] has drawn attention.
Higgs gives his version of the history here, and refers to the “Anderson mechanism”, writing:
During October 1964, Higgs had discussions with Gerald Guralnik, Carl Hagen and Tom Kibble, who had discovered how the mass of non-interacting vector bosons can be generated by the Anderson mechanism.
Guralnik, Hagen and Kibble had been working on what Higgs calls the “Anderson mechanism” and Anderson the “Anderson-Higgs mechanism”, writing a paper about it for submission to PRL. Guralnik gives his version of the history here (writing about the “Brout, Englert, Guralnik, Hagen, Kibble, Higgs phenomenon”, Higgs last, no Anderson), Kibble’s is here. In Guralnik’s version:
as we were literally placing the manuscript in the envelope to be sent to PRL, Kibble came into the office bearing two papers by Higgs and the one by Englert and Brout. These had just arrived in the then very slow and unreliable (because of strikes and the peculiarities of Imperial College) mail. We were very surprised and even amazed. We had no idea that there was any competing interest in the problem, particularly outside of the United States. Hagen and I quickly glanced at these papers and thought that, while they aimed at the same point, they did not form a serious challenge to our work.
His explanation for why they did not refer to Anderson is:
At the same time, Kibble brought our attention to a paper by P.W. Anderson [26]. This paper points out that the theory of plasma oscillations is related to Schwinger’s analysis of the possibility of having relativistic gauge invariant theories without massless vector particles. It suggests the possibility that the Goldstone theorem could be negated through this mechanism and goes on to discuss “degenerate vacuum types of theories” as a way to give gauge fields mass and the necessity of demonstrating that the “necessary conservation laws can be maintained.” In general these comments are correct. However, as they stand, they are entirely without the analysis and verification needed to give them any credibility. These statements certainly did not show the calculational path to realize our theory and hence the unified electroweak theory. It certainly did not even suggest the existence of the boson now being searched for at Fermi lab and LHC. The actual verification that the same mechanism actually worked in non-relativistic condensed-matter theories as in relativistic QFT had to wait for the work of Lange [28], which was based on GHK. We did not change our paper to reference the Anderson work.
See Guralnik’s paper for a detailed discussion of those points which he feels Anderson, Brout, Englert and Higgs had missed about all this. It remains true that the full understanding of how this works non-perturbatively is rather tricky, especially in the chiral, non-perturbative context that is relevant to the Standard Model. It may very well be that there is some important piece of understanding about this that has been missing and will someday lead to a final understanding of the origin of electroweak symmetry breaking.
Update: For two other recent expository articles about this subject and its history, see here and here.
