Para, pseudo, and orthosupersymmetric quantum mechanics and their bosonization

TL;DR

This paper explores bosonization of supersymmetric quantum mechanics and its variants using deformed Heisenberg algebras and their generalizations, enabling realization with only bosonic operators.

Contribution

It introduces a method to bosonize SSQM and its variants through algebraic generalizations, expanding the toolkit for quantum algebra representations.

Findings

Bosonization of SSQM achieved via Calogero-Vasiliev algebra

Extension to SSQM variants using $C_{ ext{lambda}}$-extended oscillator algebras

Realization of supersymmetric systems with purely bosonic operators

Abstract

We consider the problem of bosonizing supersymmetric quantum mechanics (SSQM) and some of its variants, i.e., of realizing them in terms of only boson-like operators without fermion-like ones. In the SSQM case, this is realized in terms of the generators of the Calogero-Vasiliev algebra (also termed deformed Heisenberg algebra with reflection). In that of the SSQM variants, this is done by considering generalizations of the latter algebra, namely the $C_{\lambda}$-extended oscillator algebras, where $C_{\lambda}$ is the cyclic group of order~$\lambda$.