Supersymmetry and Quasi-Supersymmetry

Summary

I first met Murray Gell-Mann when he popped up in my office at the Institute for Advanced Study, and described to me the isospin-strangeness rule he had discovered. He pronounced my name correctly and interpreted its meaning correctly. That was September 1953.

The post-War decades have been the Golden Age of particle physics. Theory and experiment went hand in hand to make amazing advances. What we know now about the world of elementary particles is incredibly richer than what we did forty years ago, and we owe this to Murray above all. Looking beyond the Baroque period we are in now, I hope Murray's spirit will come back alive again.

Recently I have been taking a renewed interest in the BCS mechanism as a model for spontaneous generation of fermion mass and associated Goldstone (G) and Higgs (H) collective bosons. Here I mean by a BCS mechanism the formation of fermion pair condensates due to a short range attraction. In an idealized situation, this may be represented by a four-fermion interaction, and the dynamics is essentially determined by the properties of fermion bubble diagrams. A characteristic feature of the bubble approximation is that the Bogoliubov–Valatin (BV) fermion and the Higgs boson have the simple mass ratio 1:2. Such modes are known to exist in superconductors.

These low energy modes can be represented by an effective Ginzburg–Landau– Gell-Mann-Lévy Hamiltonian in which the boson self-coupling and the boson-fermion Yukawa coupling are related so as to satisfy the mass ratios.