Spectrum Degeneracy of General (p=2)--Parasupersymmetric Quantum Mechanics and Parasupersymmetric Topological Invariants

TL;DR

This paper analyzes the energy spectrum degeneracy in general (p=2) parasupersymmetric quantum mechanics, revealing universal features and introducing a new topological invariant analogous to the Witten index.

Contribution

It demonstrates that the degeneracy structure is independent of Hamiltonian details and introduces a novel topological invariant for a subclass of systems.

Findings

Degeneracy structures are identical in R-S and B-D formulations.

Results are valid for arbitrary systems on any dimensional manifold.

A new topological invariant similar to the Witten index is proposed.

Abstract

A thorough analysis of the general features of $(p=2)$ parasupersymmetric quantum mechanics is presented. It is shown that for both Rubakov--Spiridonov and Beckers--Debergh formulations of $(p=2)$-parasupersymmetric quantum mechanics, the degeneracy structure of the energy spectrum can be derived using the defining parasuperalgebras. Thus the results of the present article is independent of the details of the Hamiltonian. In fact, they are valid for arbitrary systems based on arbitrary dimensional coordinate manifolds. In particular, the Rubakov--Spiridonov (R-S) and Beckers--Debergh (B-D) systems possess identical degeneracy structures. For a subclass of R-S (alternatively B-D) systems, a new topological invariant is introduced. This is a counterpart of the Witten index of the supersymmetric quantum mechanics.