Parasupersymmetric quantum mechanics of order three and a generalized witten index

Abstract

In this paper we generalize the Rubakov-Spiridonov parasupersymmetry algebra to the order three case. We also generalize the notion of the Witten index, and we provide a class of models satisfying our parasupersymmetry algebra. Finally, we show that there is a correspondence between the Hamiltonian and the index in our class of models.