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The Stanford meeting of The American Physical Society

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Electromagnetism, PCAC and global symmetry

Murray Gell-Mann
Scientist

Views | Duration | ||
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81. Electromagnetism, PCAC and global symmetry | 832 | 03:23 | |

82. The Stanford meeting of The American Physical Society | 835 | 01:55 | |

83. Muon and electron neutrinos | 868 | 01:12 | |

84. Collaborating with Feynman | 2818 | 02:40 | |

85. Global symmetry. Yang-Mill's theory. Phil Anderson | 1260 | 03:21 | |

86. Symmetry schemes | 763 | 03:16 | |

87. The Sakata model. A field theory model | 1082 | 02:28 | |

88. London and Paris. Partially conserved axial vector current | 721 | 02:31 | |

89. The Sigma model | 780 | 00:59 | |

90. Sheldon Glashow. The SU(2) times U1 theory | 1164 | 04:10 |

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[Q] *Were you thinking at that time, I mean, either about the possibility, now that you had a conserved vector current, of unification ‘quote’, with electromagnetism, or... and alsoabout PCAC? Was that already sort of in the back of your mind?*

Well, not exactly, but a little bit, in the following sense. If the vector current was isotopic spin–that couldn't be an isolated fact in my opinion–it had to be that the actual vector current was also an important quantity, a sort of axial pseudo-scalar isotopic spin with some important role to play. And then there was also a strangeness changing part, and that had to be important; that strangeness changing operator and the gamma five analogue had to be important operators as well. And these had to form a group of some kind, only I didn't think of it as a group–I meant a closed algebraic system. I had completely forgotten all that I had learned about group theory. I had studied group theory as an undergraduate taking graduate math courses at Yale. Then Racah or R'cah had given lectures, very learned lectures on group theory at the Institute for Advanced Study, which I attended; but I'd completely forgotten the whole thing, and I didn't think in terms of groups and I'd completely forgotten the Planck RA classification and all of these things. So I just thought in terms of closed algebraic systems and I thought the closed algebraic systems–closed under commutation–would have to be worked out by hand, it didn't occur to me that they were all tabulated and so on. It's really unfortunate because I could have had all these ideas much clearer at a much earlier time. But the idea that these, all these operators would have to form a closed algebraic system, closed under commutation, was very important to me, right away.

[Q] That was already..?

Right away! *I see.* Right away. As soon as we had the CVC. *Yes, yes. *So this was in late ’57.

[Q] *I see. So well before the thinking about the eightfold way and quarks?*

Oh yes. *Obviously.* Oh yes. I felt there had to be...

[Q] *In spite of the fact that it waited for that before it became sort of a tool?*

Well, also I proposed in that same year a higher symmetry with further operators. I proposed this global symmetry as a way of understanding the relations among the nucleon lambda, sigma and psi, and I got a mass formula. The mass formula was slight–very similar to the eightfold way mass formula but with the three and the one interchanged.

[Q] *Two and the one?*

Three and the one.

[Q*] Isn’t it two and the one?*

Three and the one. *Yes?* Instead of three M lambda plus M sigma over four... *It’s the other way... ...*equals M nucleon plus M psi over two: the three and the one were the other way round. And I knew, in fact, that the formula would be better if the three and the one were interchanged, but I didn't of course know how to get it. *But you had to wait for SU(3) of course ...* I didn't know how to get there, yes.

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.

**Title: **Electromagnetism, PCAC and global symmetry

**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:**
Yale University, Institute for Advanced Study, Giulio Racah

**Duration:**
3 minutes, 24 seconds

**Date story recorded:**
October 1997

**Date story went live:**
24 January 2008