Parasupersymmetric Quantum Mechanics of Order 3 and a Generalized Witten Index

TL;DR

This paper extends parasupersymmetry algebra to order 3, generalizes the Witten index, and explores models where the Hamiltonian and index are related, advancing theoretical understanding of parasupersymmetric quantum systems.

Contribution

It introduces a generalized parasupersymmetry algebra of order 3 and a corresponding Witten index, along with models satisfying this algebra and their Hamiltonian-index relationship.

Findings

Generalized parasupersymmetry algebra to order 3

Defined a new class of models satisfying the algebra

Established a correspondence between Hamiltonian and index

Abstract

In this paper we generalize the Rubakov-Spiridonov parasupersymmetry algebra to the order 3 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.