Parasupersymmetric quantum mechanics and its infinite order limit

Abstract

We propose an alternative formulation of parasupersymmetric quantum mechanics (PSQM) of arbitrary order which is simpler than the earlier versions and which leads to an explicit expression for the Hamiltonian in terms of the supercharge Q: H=½[(Q^†Q)²+(QQ^†)²-QQ ^†Q^†Q]^½. We also use it to construct the PSQM of infinite order whose algebra corresponds to that of Greenberg's infinite statistics. A model of conformal PSQM in which dilatation and conformal generators are analogously expressed in terms of the conformal supercharges is constructed.