N= 4 Supersymmetric Quantum Mechanical Model: Novel Symmetries

TL;DR

This paper explores novel discrete symmetries in an N=4 supersymmetric quantum mechanical model of a charged particle on a sphere with a magnetic monopole, linking symmetries to differential geometry concepts.

Contribution

It introduces new discrete symmetries and geometrical interpretations of N=4 SUSY transformations using supervariable approach.

Findings

Identification of novel discrete symmetries

Realization of de Rham cohomological operators

Geometrical interpretation of SUSY transformations

Abstract

We discuss a set of novel discrete symmetry transformations of the N = 4 supersymmetric quantum mechanical model of a charged particle moving on a sphere in the background of Dirac magnetic monopole. The usual five continuous symmetries (and their conserved Noether charges) and two discrete symmetries together provide the physical realizations of the de Rham cohomological operators of differential geometry. We have also exploited the supervariable approach to derive the nilpotent N = 4 SUSY transformations and provided the geometrical interpretation in the language of translational generators along the Grassmannian directions onto (1, 4)-dimensional supermanifold.