Novel symmetries in N = 2 supersymmetric quantum mechanical models

Abstract

We demonstrate the existence of a novel set of discrete symmetries in the context of N = 2 supersymmetric (SUSY) quantum mechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic oscillator. We perform the same exercise for the motion of a charged particle in the X-Y plane under the influence of a magnetic field in the Z-direction. We derive the underlying algebra of the existing continuous symmetry transformations (and corresponding conserved charges) and establish its relevance to the algebraic structures of the de Rham cohomological operators of differential geometry. We show that the discrete symmetry transformations of our present general theories correspond to the Hodge duality operation. Ultimately, we conjecture that any arbitrary N = 2 SUSY quantum mechanical system can be shown to be a tractable model for the Hodge theory.

LaTeX file, 23 pages, Title and Abstract changed, Text modified, version to appear in Annals of Physics

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Cited by in corpus (13)

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• N = 2 SUSY symmetries for a moving charged particle under influence of a magnetic field: Supervariable approach
• A Free N = 2 Supersymmetric System: Novel Symmetries
• Supervariable approach to nilpotent symmetries of a couple of N = 2 supersymmetric quantum mechanical models
• Augmented Superfield Approach to Nilpotent Symmetries in the Modified Version of 2D Proca Theory
• Novel symmetries in an interacting N = 2 supersymmetric quantum mechanical model
• Canonical brackets of a toy model for the Hodge theory without its canonical conjugate momenta
• N = 2 Supersymmetric Harmonic Oscillator: Basic Brackets Without Canonical Conjugate Momenta
• 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
• Coupled $\mathcal{N}$ = 2 supersymmetric quantum systems: symmetries and supervariable approach