## Murray Gell-Mann - Departmental interaction holds the key (91/200)

Uploader: Web of Stories - Life Stories of Remarkable People

Original upload date: Thu, 19 May 2016 00:00:00 GMT

Archive date: Wed, 24 Nov 2021 20:05:20 GMT

To listen to more of Murray Gell-Mann’s stories, go to the playlist: https://www.youtube.com/playlist?list=PLVV0r6CmEsFxKFx-0lsQDs6oLP3SZ9BlA
New York-born physicist Murray Gell-Mann (1929-2019) was

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a theoretical physicist. His considerable contributions to physics include the theory of quantum chromodynamics. He was awarded the 1969 Nobel Prize in Physics for his work on the theory of elementary particles. [Listener: Geoffrey West]
TRANSCRIPT: I realized that in modern notation you could have SU(2) times SU(2); you could have SU(2) times SU(2) times SU(2); you could have SU(2) times U1; you could have SU(2) times U1 times U1; SU(2) times SU(2) times U1 and so on and forth–any product of SU(2)s and U1s, as we would phrase it today, would be a possible group, and the corresponding algebra would be the right algebra. That would be fine. But was there anything else? Well, I worked on it, by brute force. I'd totally forgotten everything I'd learned about Lie algebras and so on and… That's trivial!… I worked on it—trivial! But I worked on it–in this academic year ’59-60, particularly in the fall of ’59, I worked on it every afternoon. But the problem was every noon, when I was working at the Collège de France I would go across the street to Les Trois Bourriques [sic] and have lunch with a lot of excellent French red wine, and after the lunch with the wine I would sit there in my office trying to work out whether there was a solution with five operators, with six operators, with seven operators. And I showed that there was up to seven there was nothing but SU(2)s and U1s. And the thought after all that wine of going on to eight was just too much! What was particularly amusing was that a lot of the time one of my companions at lunch was a professor at the Collège de France named Serre, who was probably the world's greatest expert on Lie algebras and Lie groups. But even if I had shown him the problem, it wouldn't have done the least good because he would not have recognized in this practical form the things that he worked with every day, because he treated them so abstractly. So I didn't know during that whole year whether there was really something beyond SU(2) and U1. But of course, if I had taken the trouble to remember, or if I… if I'd remembered about Lie algebras and so on, I would have had it immediately. Getting to eight, which I hadn't tried, I'd gotten only as far as seven, getting to eight, there would have been a new solution, namely SU(3), which is not made up of SU(2) and U1.
Well, my enlightenment about this issue came then a year late, in the fall of 1960 when I returned from Africa, from Europe and Africa, gave my talk on Shelly's ideas and some talk on my ideas as well, at Rochester, and then went back to Caltech. I found an Assistant Professor of Mathematics in our building–actually it was a new building which we shared, which some of us physicists shared with mathematicians, so it promoted interaction between physicists and mathematicians–I found an Assistant Professor of Mathematics named Block, Dick Block, and I asked him whether he'd ever seen such equations. And he said, ‘Oh, that's a canonical form for a product, for a… the Lie algebra associated with the product of simple Lie groups. That's all it is. You just… and the simple Lie groups have been classified, so all the solutions to this problem are known.’ So in… in two to three sentences he cleared up the whole matter. Well, I looked at the next one, SU(3), and it looked beautiful. And by Christmas I had understood how to do the whole thing and I went out to the desert for New Year’s Eve, returning I think, the day after New Year’s Day and started to work out the whole idea of the Eightfold Way.