Integrals of motion, supersymmetric quantum mechanics and dynamical supersymmetry

TL;DR

This paper explores how classical symmetries in relativistic and non-relativistic particles lead to supersymmetric quantum mechanics and dynamical supersymmetry, with potential implications for high-temperature superconductivity.

Contribution

It demonstrates the emergence of supersymmetry at specific parameter values in classical particle models and introduces quantum dynamical supersymmetry through coupling to gauge fields.

Findings

Classical symmetries determine parameter quantization.

Supersymmetry appears at special coupling constants.

Dynamical supersymmetry may relate to high-temperature superconductivity.

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.