The genesis of unified gauge theories by Tom Kibble

Abdus Salam in Munich, 1947.

The theoretical physics group at London's Imperial College in 1959 From 8-12 March, at a had three permanent faculty: Abdus 'Salamfest' at the International Salam, his erstwhile thesis supervi­ Centre for Theoretical Physics in sor Paul Matthews, and John Trieste, Italy, friends, colleagues, C.Taylor. I joined as a lecturer the admirers and former students paid following year. tribute to the Institute's founder In those early days we had lots of and director Abdus Salam, and his visitors, both long- and short-term - contributions to science. Presenta­ Murray Gell-Mann, Ken Johnson, tions centred around the develop­ John Ward, Lowell Brown, Gordon ment of today's Standard Model of Feldman and Steven Weinberg. particle physics and attempts to go About a year after I arrived we were beyond it, and the parallels be­ transferred from the Mathematics to tween the physics of condensed the Physics Department under the matter and elementary particles. formidable Patrick (P.M.S.) Blackett. During the week, Salam was Having been brought up in the awarded the honorary degree of Cavendish Laboratory tradition under Doctor of Science by the Rector of Lord Rutherford, Blackett was rather St. Petersburg University, Acad­ scornful of theoretical physicists, but emician S. Merkuriev. he knew a good thing when he saw states of a single fundamental entity, While in recent years Salam has one and had persuaded Salam to join the nucléon. The symmetry was mainly been identified with the the rapidly expanding Physics De­ generalized to include Yukawa's Centre which he established in partment. mesons in an important paper by 1964, many of his important In 1960 field theory was widely Nick Kemmer in 1938, which is contributions to physics came regarded as very passé. It had had incidentally perhaps one of the first when he resided permanently at its triumphs: renormalization theory papers to suggest the need for a London's Imperial College. At the had made sense of divergences, and neutral current. Trieste Salamfest, Tom Kibble, quantum electrodynamics had been Kemmer was very influential in formerly Head of Physics at magnificently vindicated. British theoretical physics in the Imperial and a longtime colleague But field theory didn't seem to work immediate post-war period. He was of Salam, described Salam's role for anything else, particularly not for Paul Matthews' supervisor in Cam­ at Imperial in the quest for a the strong interactions, and was bridge and when I was a student in unification of electromagnetism definitely out of fashion. There were, Edinburgh he was my Head of and the weak force. In 1979 however, a few places in the world Department, having succeeded Max Salam, Sheldon Glashow and where field theory was still studied Born in 1953. Steven Weinberg shared the unashamedly. Imperial College was In the forties and fifties, as new Nobel Physics Prize for the new one. Harvard was certainly another; particles proliferated, it was natural to synthesis, one of the major many of our visitors over the next few try to bring some order into this achievements of 20th-century years were Julian Schwinger's chaos by enlarging the symmetry physics. students. group beyond the SU(2) of isospin, (This is an abridged version of At Imperial there were two dominant especially after the discovery of the the talk, the complete version theory themes: symmetries and new quantum number, strangeness. being available on request from gauge theories. Both had their Salam had students working on Tom Kibble at the Blackett Labora­ origins in the concept of isospin. every conceivable symmetry group. tory, Imperial College, London, The isospin symmetry between One of those students was Yuval SW7). protons and neutrons had shown Ne'eman, who had the good fortune how two apparently disparate parti­ and/or prescience to work on SU(3). cles might be regarded as different From that work, and of course from

22 CERN Courier, June 1993 The International Centre for Theoretical Physics, Trieste, Italy was founded byAbdus Salam in 1964. the independent work of Murray Gell- Mann, stemmed the Eightfold Way, with its triumphant vindication in the discovery of the omega-minus in 1964. Salam himself made many impor­ tant contributions to these symmetries, but I believe this was not his first love. His real goal was to find the ultimate theory to describe the weak, electromagnetic and strong interactions, and even gravity - what we would now call a Theory of Everything. From an early stage, certainly well before I joined Imperial, Salam was convinced that the ultimate theory would be a gauge theory. The starting point was the epoch- making paper of Yang and Mills in 1954. There may be others who deserve some of the credit - Weyl, hard to make progress because and Feynman and Gell-Mann Klein, Shaw, Utiyama - but Yang and calculations were difficult. With such showed how the weak interaction Mills articulated very clearly the a strong coupling, perturbation theory should be written down. This sug­ 'gauge principle' - sometimes para­ would not work, and the asymptotic gested that weak interactions could phrased as 'Nature abhors a rigid freedom of quarks was unknown. be mediated by a charged vector symmetry'. So the weak interactions emerged boson, the W. Yang and Mills argued that a rigid, as a better bet. There were certainly The seemingly insuperable difficulty global isospin symmetry is incompat­ tantalizing hints of a structure very was the large W mass. If the interac­ ible with relativistic field theory. Their similar to electrodynamics. While tion were of the same strength as point was that once isospin symmetry Fermi's classic recipe with four electromagnetism, the W mass would has been accepted, it is arbitrary particles interacting at a point was have to be about 40 GeV. But which component is identified with obviously non-renormalizable, it was putting a mass term in the the proton and which with the neu­ probably a shorthand way of writing Lagrangian would destroy the gauge tron. But it then seems odd that an effective interaction due to the invariance, and the heavy vector making this choice should automati­ exchange of a heavy boson. particle would make the formalism cally fix the convention throughout all Progress was held up while people blow up and become unrenorm- space for ever. So they looked at searched for the correct space-time alizable. what needed to be done to make symmetry of the weak interaction. As early as 1958, Salam and John isospin a local symmetry. The breakthrough came with another Ward proposed a unified gauge The gauge principle provided a suggestion of Yang's, working this theory of weak and electromagnetic natural basis for electromagnetic time with T.D. Lee, that mirror sym­ interactions, involving a charge triplet interactions, and after the work of metry (parity) is not conserved in of vector mesons, with the neutral Yang and Mills people began to look weak interactions. After the fall of component identified with the photon. for gauge theories of the strong and parity in 1957, Salam was one of the They placed the electron, neutrino weak interactions. first to point out the connection and positron too in a triplet. This was The first goal was strong interac­ between left-handedness and a zero ingenious, but of course they could tions; that is what Yang and Mills mass neutrino. only obtain the parity-conserving part themselves were after. But it was Meanwhile Marshak and Sudarshan of the weak interaction. Parity

CERN Courier, June 1993 23 Abdus Salam at Stockholm in 1979 - the first Pakistani to receive the Nobel Award. violation was artificially imposed, and Guralnik and Dick Hagen, both at the W mass put in by hand. Imperial that year, and I had also Two years later they proposed a realized the Goldstone theorem unified theory of weak, electromag­ doesn't apply to gauge symmetries, netic and strong interactions, based others were there too. The result on the gauge group SO(8), a paper was published independently in 1964 well ahead of its time, foreshadowing by Englert and Brout and by Peter later ideas of grand unification. Higgs. But these theories did not really So by 1963*64 the problem of the work; nor did similar ones proposed origin of mass was solved, at least in by Glashow and others. The major principle. But there was still another obstacle remained the vector meson major hurdle, to unify weak interac­ mass. This was essential to make tions, which are parity-violating, with the interaction weak and short-range, electromagnetism, which is not. It but apparently incompatible with both took another three years to realize gauge invariance and that for the photon to coexist with the renormalizability. The only way parity violation of weak interactions, anyone knew to make a vector- the gauge group had to be extended meson theory renormalizable was to from SU(2) to SU(2)xU(1), with two use zero-mass gauge bosons. neutral particles rather than one. As often happens, progress was Actually the solution, or something delayed by a 'folk theorem'. Theo­ very like it, was already there in retical physicists sometimes quote Sheldon Glashow's 1961 paper 'theorems' that everyone believes but forces. But the theorem seemed to which had proposed SU(2)xli(1) with eventually turn out not to be true. rule out this mechanism for relativis­ mixing between the neutral particles, One such folk theorem was that the ts theories. but this was before the key concepts photon is massless because of An important 1963 paper by Phil of spontaneous symmetry breaking gauge invariance, considered one of Anderson showed how Schwinger's and the Higgs mechanism had been the predictive successes of the suggestion of a heavy gauge field developed. gauge principle. In 1961 Julian could work. One example was the At Imperial, Salam kept plugging Schwinger said this theorem might plasmon: in a high-density plasma away at the problem, especially in be false, although he was thinking the photon acquires a non-zero collaboration with John Ward. In more about strong interactions at the 'mass' - the plasma frequency. But autumn 1967, Salam gave a series of time. Anderson also pointed out, using the lectures at Imperial in which he Another folk theorem came in when example of superconductivity, how described the SU(2)xU(1) theory. people began edging towards spon­ Goldstone bosons could 'become Meanwhile the same model had been taneous symmetry breaking to tangled up with Yang-Mills gauge found independently by Steven explain the heavy gauge mesons. bosons and, thus, do not in any true Weinberg. Here the Goldstone theorem appar­ sense have zero mass'. He con­ When Weinberg's paper appeared I ently predicted unobserved massless cluded 'the Goldstone zero-mass was at Rochester, where Bob spin-zero particles. difficulty is not a serious one, be­ Marshak asked me to give a talk to When Steven Weinberg came to cause we can probably cancel it off his weekly discussion group. Imperial College in 1961-62, he and against an equal Yang-Mills zero- I mentioned that Salam and Ward Salam, collaborating at long range mass problem'. This is exactly what had been working on very similar with Jeffrey Goldstone, spent a lot of is now known as the Higgs mecha­ ideas, and focused on the problems time confirming this theorem. In nism. in constructing a unified theory of condensed-matter physics, This should have cleared everything weak and electromagnetic interac­ counterexamples to the Goldstone up, but these new ideas were difficult tions and how ingeniously the new theorem were known for long-range to understand. By the time Gerry model avoided them. However I

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CERN Courier, June 1993 25 described it as a wonderful toy - First crumb of research without any connection to the real world! While I was myopic, in a sense I In 1964, Abdus Salam introduced only to a privileged few. was right. The whole thing seemed Paul Matthews' inaugural lecture at Later, his PhD complete, Matthews much too ad hoc and ugly, with its London's Imperial College. It was a left a research 'crumb', as Salam put curious built-in asymmetry between poignant moment. Salam, who had it. The agreement was that Salam the left- and right-handed fermions taken his first steps in theoretical would look at a continuing problem in and its large number of independent physics at Cambridge under meson field fenormalization while parameters. If it is part of the final Matthews' watchful eye, had become Matthews took a few months off theory, it is ugly; surely the Creator Imperial's first professor in Theoreti­ before starting work at Princeton in was having an off day! But that is not cal Physics. Now he was overseeing the fall. If Salam had made no the right way to look at it. Seen the promotion of his former supervi­ progress, Matthews would repossess merely as one step towards a still sor. the problem. undiscovered final theory, the intri­ Salam recalled his 1949 research Characteristically, Salam's first act cate way the electroweak picture fits debut at Cambridge, where, because as a research student was to phone together does have a remarkable of impressive examination results, he Freeman Dyson (his 'hero'), then beauty. had initially been directed towards visiting Birmingham, and ask for an It is sad that Paul Matthews, who the laboratory. interview. The discussion continued died tragically six years ago, could 'Soon, I knew the craft of experi­ on the train to Southampton, where not have given this tribute. For many mental physics was beyond me, ' Dyson was to embark for the US. years, Imperial was Salam and wrote Salam later. It was the sublime The seeds of the solution were sown Matthews. They made a superb quality of patience which I lacked.' and soon the 'crumb' problem was team, exactly complementing each Looking towards theory, he had gone solved. It was the start of a meteoric other's strengths and abilities. to Nicholas Kemmer (in the front row career. at Matthews' inaugural). Kemmer had said he had enough students already Paul Matthews (1919-1987). Abdus Salam's and did not want another. Salam had first mentor. pleaded, and fortunately Kemmer had relented. 'All theoretical problems in quantum electrodynamics have been solved by Schwinger, Feynman and Dyson, ' Kemmer had told Salam. 'Paul Matthews has applied their methods to meson theories. He is finishing his PhD. Ask him.' At Imperial in 1964, Salam recalled that first meeting with Matthews in 1950. What are you reading?' Matthews had asked. 'Heitler's Quantum Theory of Radiation, ' had come the reply. It was the only standard text at the time. Matthews quickly recommended instead the new work by Schwinger, Feynman and Dyson, then known

26 CERN Courier, June 1993