N = 2 SUSY symmetries for a moving charged particle under influence of a magnetic field: Supervariable approach

Abstract

We exploit the supersymmetric invariant restrictions (SUSYIRs) on the supervariables to derive the nilpotent N = 2 SUSY transformations for the supersymmetric quantum mechanical model of the motion of a charged particle in the X-Y plane (where the magnetic field (B_z) is applied along the Z-direction). The supervariables are defined on a (1, 2)-dimensional supermanifold parametrized by a bosonic "time" variable t and a pair of Grassmannian variables \theta and \bar\theta (with \theta^2 = {\bar\theta}^2 = 0, \theta\bar\theta + \bar\theta\theta = 0). We take the (anti-)chiral supervariables for our purpose so that the nilpotency property of the N = 2 SUSY symmetry transformations could be captured within the framework of supervariable approach. We express the Lagrangian as well as supercharges in terms of the supervariables (that are obtained after the application of the appropriate SUSYIRs) and provide geometrical basis, within the framework of our supervariable approach, for (i) the nilpotency property of the above SUSY transformations, and (ii) the SUSY invariance of the Lagrangian.