Reducibility and bosonization of parasupersymmetric and orthosupersymmetric quantum mechanics

TL;DR

This paper demonstrates that order-$p$ parasupersymmetric and orthosupersymmetric quantum mechanics can be fully reduced and bosonized using generalized deformed oscillator algebra and ${ m Z}_{p+1}$-grading, providing minimal bosonization.

Contribution

It introduces a method to fully reduce and bosonize parasupersymmetric and orthosupersymmetric quantum mechanics using generalized deformed oscillator algebra and ${ m Z}_{p+1}$-grading.

Findings

Full reducibility of order-$p$ parasupersymmetric and orthosupersymmetric quantum mechanics.

Construction of $p+1$ sets of bosonized operators.

Minimal bosonization scheme for these quantum systems.

Abstract

Order-$p$ parasupersymmetric and orthosupersymmetric quantum mechanics are shown to be fully reducible when they are realized in terms of the generators of a generalized deformed oscillator algebra and a ${\rm Z}_{p+1}$-grading structure is imposed on the Fock space. The irreducible components provide $p+1$ sets of bosonized operators corresponding to both unbroken and broken cases. Such a bosonization is minimal.