A free supersymmetric system: Novel symmetries

Abstract

We discuss a set of novel discrete symmetries of a free supersymmetric (SUSY) quantum-mechanical system which is the limiting case of a widely studied interacting SUSY model of a charged particle constrained to move on a sphere in the background of a Dirac magnetic monopole. The usual continuous symmetries of this model provide the physical realization of the de Rham cohomological operators of differential geometry. The interplay between the novel discrete symmetries and usual continuous symmetries leads to the physical realization of the relationship between the (co-)exterior derivatives of differential geometry. We have also exploited the supervariable approach to derive the nilpotent SUSY symmetries of the theory and provided the geometrical origin and interpretation for the nilpotency property. Ultimately, our present study (based on innate symmetries) proves that our free SUSY example is a tractable model for the Hodge theory.