Integrals of motion, supersymmetric quantum mechanics and dynamical supersymmetry

Abstract

The class of relativistic spin particle models reveals the `quantization' of parameters already at the classical level. The special parameter values emerge if one requires the maximality of classical global continuous symmetries. The same requirement applied to a non-relativistic particle with odd degrees of freedom gives rise to supersymmetric quantum mechanics. Coupling classical non-relativistic superparticle to a `U(1) gauge field', one can arrive at the quantum dynamical supersymmetry. This consists in supersymmetry appearing at special values of the coupling constant characterizing interaction of a system of boson and fermion but disappearing in a free case. Possible relevance of this phenomenon to high-temperature superconductivity is speculated.

Comments: 6 pages, LaTeX. Based on invited talk given at the International Seminar "Supersymmetries and Quantum Symmetries" dedicated to the memory of Victor I. Ogievetsky (Dubna, July 22-26, 1997); to be published in Proceedings