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The Yang-Mills theory


Another visit to The Institute for Advanced study. Shiing-Shen Chern
Murray Gell-Mann Scientist
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I visited the Institute for Advanced Study again in… for the spring term of 1955. I was on leave from Chicago in the fall at Columbia where they were offering me a tenured associate professorship and that's when I became engaged to Margaret. I had met her in the spring at the Institute for Advanced Study where she worked as the assistant to a lady archaeology professor, and when she came back from England in the fall we saw each other a great deal and we became engaged in November or so. And I decided I didn't want to go back to Chicago right away, I wanted to spend the spring at the Institute for Advanced Study, which I did. And that was when, as I described, when Einstein died and they took pictures of Margaret along with the institute and so on. Well, the Yang-Mills theory was very new at that time, in the spring of ’55. I was quite interested in it, but an incident occurred that impressed me very much with the situation in mathematics and the relation between mathematics and science. SS Chern was visiting Princeton then. He was a very famous mathematician working at Berkeley and he had been Frank Yang's teacher in China. They knew each other very, very well. They spent a lot of time together, their children played together; their wives saw each other and so on and so forth, during that spring in Princeton. Well, Frank spoke once or twice about the Yang-Mills theory, which was quite new. And SS Chern gave a series of lectures in the other building on mathematics, speaking on fiber bundles. And the number of physicists who were mathematically inclined attended the lectures on fiber bundles. But even at the end of that lecture series, and even after Frank had given a talk or two on the Yang-Mills theory, no one realized that these were the same thing… essentially the same thing; that the Yang-Mills theory was a special case of a fiber bundle, a non-trivial fiber bundle. And this despite the fact that Frank and Chern were so close together, they –I mean so close, such close friends and such close associates. They saw each other all the time, each one explained his ideas and neither of them realized that these ideas were essentially the same. It's amazing. But it's a consequence of the mood in mathematics at that time.

New York-born physicist Murray Gell-Mann (1929-2019) was known for his creation of the eightfold way, an ordering system for subatomic particles, comparable to the periodic table. His discovery of the omega-minus particle filled a gap in the system, brought the theory wide acceptance and led to Gell-Mann's winning the Nobel Prize in Physics in 1969.

Listeners: Geoffrey West

Geoffrey West is a Staff Member, Fellow, and Program Manager for High Energy Physics at Los Alamos National Laboratory. He is also a member of The Santa Fe Institute. He is a native of England and was educated at Cambridge University (B.A. 1961). He received his Ph.D. from Stanford University in 1966 followed by post-doctoral appointments at Cornell and Harvard Universities. He returned to Stanford as a faculty member in 1970. He left to build and lead the Theoretical High Energy Physics Group at Los Alamos. He has numerous scientific publications including the editing of three books. His primary interest has been in fundamental questions in Physics, especially those concerning the elementary particles and their interactions. His long-term fascination in general scaling phenomena grew out of his work on scaling in quantum chromodynamics and the unification of all forces of nature. In 1996 this evolved into the highly productive collaboration with James Brown and Brian Enquist on the origin of allometric scaling laws in biology and the development of realistic quantitative models that analyse the influence of size on the structural and functional design of organisms.

Tags: Institute for Advanced Study, Princeton University, University of Chicago, Columbia University, University of California, Berkeley, China, Albert Einstein, SS Chern, Frank Yang

Duration: 3 minutes, 15 seconds

Date story recorded: October 1997

Date story went live: 24 January 2008