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

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 θand \barθwith θ^2 = \barθ^2 = 0, θ\barθ+ \barθθ= 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.

LaTeX file, 19 pages, Journal reference

References in corpus (4)

• An Alternative To The Horizontality Condition In Superfield Approach To BRST Symmetries
• A Generalization Of The Horizontality Condition In The Superfield Approach To Nilpotent Symmetries For QED With Complex Scalar Fields
• Novel discrete symmetries in the general N = 2 supersymmetric quantum mechanical model
• Novel symmetries in N = 2 supersymmetric quantum mechanical models

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• Canonical brackets of a toy model for the Hodge theory without its canonical conjugate momenta
• Nilpotent Charges in an Interacting Gauge Theory and an N = 2 SUSY Quantum Mechanical Model: (Anti-)Chiral Superfield Approach
• Nilpotent Charges of a Toy Model of Hodge Theory and an $\mathcal{N}$ = $2$ SUSY Quantum Mechanical Model: (Anti-)Chiral Supervariable Approach
• A Specific N = 2 Supersymmetric Quantum Mechanical Model: Supervariable Approach
• N= 4 Supersymmetric Quantum Mechanical Model: Novel Symmetries
• Revisiting Novel Symmetries in Coupled $\mathcal{N}=2$ Supersymmetric Quantum Systems: Examples and Supervariable Approach