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Quarks, mass shell analysis and the bootstrap


Investigating regge poles at MIT
Murray Gell-Mann Scientist
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Murph and I wrote a letter about that, using just second order results. But we needed to check that in higher order the same thing would hold, so we decided to check fourth order, which was very laborious. But Murph and Francis and I, using huge pieces of white paper to do our calculations and checking and re-checking every bit of arithmetic, managed to verify that indeed there was a... a moving pole. So there was no validity to the dogma. In fact, Regge trajectories existed for the so-called elementary particles of quantum field theory, the ones that were put in as fundamental fields, just as much as they did for composite objects. We had some trouble then when we tried to extend the calculation to the, what I called… what I named the Pomeranchuk trajectory. Pomeranchuk didn't believe in any of this stuff, but after I named the trajectory after him he began to like it quite a lot. And that was the trajectory going to one at zero value of the momentum transfer variable, the dominant trajectory in reactions where no quantum numbers were being exchanged. And we kept... we... Murph and Francis and I and a young man named Jeremiah Sullivan, who was I think at the University of Illinois, or went there later or something of that kind, maybe went there laterI guess and is still there now. He was with Murph at Princeton. I guess that's what he was. He was... he was a student of Murph's... A student of Murph’s. …a student of Murph's at Princeton, right. We tried to calculate and we kept getting the result that the radiative corrections pushed the value above one, which would violate unitarity. And actually that was correct result and since it violates unitarity it destroyed the character of a pole, and there were all sorts of things, interesting things thappened which we didn't pursue. They were later pursued by a… a post-doc of mine named Hoon Chang [sic] and somebody else who was–I forget who his collaborator was.

[Q]Wasn't it T T Wu?

Was it T T Wu? It was T T Wu. I thought it was TT Wu–yeah. Anyway, the two of them pursued this later on and discovered the mathematical complications. We were just puzzled. We kept thinking we must have made a mistake in sine and yet when we checked and re-checked our results we hadn't made a mistake in sine. We didn't know quite what to make of it. We should of course have pursued it further and we would have discovered these interesting mathematical phenomena associated with the Pomeranchuk singularity. Now all of that work, as far as I know, is correct; that is the work in its final form. Of course people made errors along the way, but the final form of all these results was correct. Nobody works on it much any more, but...

[Q] You mean the final form meaning the whole... the whole phenomenology and the whole understanding, the Regge poles..?

Well, the phenomenology we have not yet really understood but we... but we worked it out. Sure. We worked out the phenomenology. We worked out a lot of the theoretical properties of singularities in the complex angular momentum plane and related them to high energy behavior of reaction amplitudes, including scattering amplitudes. And eventually we got a lot of these things right. Nobody pays much attention to them any more–its funny, and yet it's a perfectly correct, perfectly valid subject, just unfashionable. Very interesting. Often when things become unfashionable it's because they were replaced by something else and proved to be wrong. But that's not the case here.

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: MIT, , Princeton University, Murph Goldberger, Francis Low, Isaak Pomeranchuk, Jeremiah Sullivan, Hoon Chang, TT Wu

Duration: 4 minutes, 28 seconds

Date story recorded: October 1997

Date story went live: 24 January 2008