Novel symmetries in an interacting 𝒩 = 2 supersymmetric quantum mechanical model

Abstract

In this paper, we demonstrate the existence of a set of novel discrete symmetry transformations in the case of an interacting [Formula: see text] supersymmetric quantum mechanical model of a system of an electron moving on a sphere in the background of a magnetic monopole and establish its interpretation in the language of differential geometry. These discrete symmetries are, over and above, the usual three continuous symmetries of the theory which together provide the physical realizations of the de Rham cohomological operators of differential geometry. We derive the nilpotent [Formula: see text] SUSY transformations by exploiting our idea of supervariable approach and provide geometrical meaning to these transformations in the language of Grassmannian translational generators on a [Formula: see text]-dimensional supermanifold on which our [Formula: see text] SUSY quantum mechanical model is generalized. We express the conserved supercharges and the invariance of the Lagrangian in terms of the supervariables (obtained after the imposition of the SUSY invariant restrictions) and provide the geometrical meaning to (i) the nilpotency property of the [Formula: see text] supercharges, and (ii) the SUSY invariance of the Lagrangian of our [Formula: see text] SUSY theory.