Wilson won the Nobel prize in 1982 for his work on critical phenomena and phase transitions, but his influence on particle theory was arguably even greater than on condensed matter physics. Unfortunately I never got a chance to meet him, but a large part of what I was learning about quantum field theory back in my days as a graduate student came either directly or indirectly from him.
Soon after the discovery of asymptotic freedom in 1973, he started work on developing lattice methods for studying gauge theories non-perturbatively with a fixed cut-off. This founded the whole field of lattice gauge theory, which remains a major and active part of HEP theory. Not many people have a whole section of the arXiv they’re responsible for. For his story of how this came about, see his 2004 The Origins of Lattice Gauge Theory.
The reason Wilson was well-placed to quickly get lattice gauge theory off the ground in 1973-4 was that he was one of very few theorists who had been thinking hard and fruitfully about the meaning of non-perturbative quantum field theory. After getting an undergraduate degree in math from Harvard in 1956, he did his thesis work under Gell-Mann at Caltech, finishing in 1961 and developing an interest in the renormalization group. From 1963 on he was focusing his research on strong interactions and the high energy behavior of quantum field theory. This was a time when QFT had fallen out of favor, with S-matrix theory considered the cutting edge. One reason others weren’t thinking about this was that the problem was very hard. It was also perhaps the deepest problem around: how do you make sense of quantum field theory? What is QFT, really, outside of the approximation method of perturbation theory?
By the early 1970s, Wilson had developed the ideas about the renormalization group and QFT that now form the foundation of how we think about non-perturbative QFTs. The first applications of this actually were to problems about critical phenomena, and it was for this work that he won the Nobel prize. With the arrival of QCD, these ideas became central to the whole field of particle theory, with much of the 1970s and early 80s devoted to investigations that relied heavily on them. If you were a graduate student then, you certainly were reading his papers.
John Preskill has a wonderful posting up about Wilson, with the title We are all Wilsonians now. He ends it by explaining Wilson’s early role in the debate about “naturalness”. Wilson was well aware of the quadratic sensitivity of elementary scalars to the cut-off and had argued that this meant that you didn’t expect to see elementary scalars at low masses. This argument was developed here by Susskind as a motivation for technicolor. Preskill doesn’t mention though that Wilson later referred to this as a “blunder”. In 2004 he had this to say:
The final blunder was a claim that scalar elementary particles were unlikely to occur in elementary particle physics at currently measurable energies unless they were associated with some kind of broken symmetry . The claim was that, otherwise, their masses were likely to be far higher than could be detected. The claim was that it would be unnatural for such particles to have masses small enough to be detectable soon. But this claim makes no sense when one becomes familiar with the history of physics. There have been a number of cases where numbers arose that were unexpectedly small or large. An early example was the very large distance to the nearest star as compared to the distance to the Sun, as needed by Copernicus, because otherwise the nearest stars would have exhibited measurable parallax as the Earth moved around the Sun. Within elementary particle physics, one has unexpectedly large ratios of masses, such as the large ratio of the muon mass to the electron mass. There is also the very small value of the weak coupling constant. In the time since my paper was written, another set of unexpectedly small masses was discovered: the neutrino masses. There is also the riddle of dark energy in cosmology, with its implication of possibly an extremely small value for the cosmological constant in Einstein’s theory of general relativity.
This blunder was potentially more serious, if it caused any subsequent researchers to dismiss possibilities for very large or very small values for parameters that now must be taken seriously…
He then goes on to argue at length that the lesson of the history of science is that often what seemed like unlikely possibilities turned out to be the right ones, with the argument for unlikeliness just a reflection of the fact that people had been making assumptions that weren’t true and/or they didn’t understand the possibilities as well as they thought they did.
Wilson may be no longer with us, but his ideas certainly are, and they’re very relevant to the biggest controversies of the day.
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