Topological generalizations of supersymmetry

Abstract

We introduce a class of generalizations of supersymmetry that involve a set of integer-valued topological invariants. These symmetries are defined in terms of certain conditions on the spectral properties of the corresponding quantum systems. We identify the operator algebras of the generators of these symmetries and show that the algebras of ordinary and fractional supersymmetric quantum mechanics and parasupersymmetric quantum mechanics of order two are special cases of these operator algebras.