Supervariable approach to nilpotent symmetries of a couple of N = 2 supersymmetric quantum mechanical models

TL;DR

This paper introduces a supervariable approach to derive and analyze nilpotent supersymmetric symmetries in N=2 SUSY quantum mechanical models, simplifying the demonstration of invariance and nilpotency.

Contribution

The authors develop a novel supervariable method to systematically derive on-shell and off-shell SUSY transformations, applicable to various N=2 SUSY quantum systems.

Findings

Successfully derived SUSY transformations for free and interacting models

Expressed Lagrangian and charges in supervariable terms demonstrating invariance

Potential for generalization to other N=2 SUSY systems

Abstract

We derive the on-shell as well as off-shell nilpotent supersymmetric (SUSY) symmetry transformations for the N = 2 SUSY quantum mechanical model of a one (0 + 1)-dimensional (1D) free SUSY particle by exploiting the SUSY invariant restrictions (SUSYIRs) on the (anti-)chiral supervariables of the SUSY theory that is defined on a (1, 2)-dimensional supermanifold (parametrized by a bosonic 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). Within the framework of our novel approach, we express the Lagrangian and conserved SUSY charges in terms of the (anti-)chiral supervariables to demonstrate the SUSY invariance of the Lagrangian as well as the nilpotency of the SUSY conserved charges in a simple manner. Our approach has the potential to be generalized to the description of other N = 2 SUSY quantum mechanical systems with physically interesting potential functions. To corroborate the above assertion, we apply our method to derive the N = 2 continuous and nilpotent SUSY transformations for one of the simplest interacting SUSY system of a 1D harmonic oscillator.