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The Eightfold Way


Departmental interaction holds the key
Murray Gell-Mann Scientist
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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…

[Q] 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 w

as 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.

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: Collège de France, Aux Trois Bourrique, Africa, Europe, Rochester, Caltech, Jean-Pierre Serre, Dick Block

Duration: 4 minutes, 3 seconds

Date story recorded: October 1997

Date story went live: 24 January 2008