Novel discrete symmetries in the general N = 2 supersymmetric quantum mechanical model

Abstract

In addition to the usual supersymmetric (SUSY) continuous symmetry transformations for the general N = 2 SUSY quantum mechanical model, we show the existence of a set of novel discrete symmetry transformations for the Lagrangian of the above SUSY quantum mechanical model. Out of all these discrete symmetry transformations, a unique discrete transformation corresponds to the Hodge duality operation of differential geometry and the above SUSY continuous symmetry transformations (and their anticommutator) provide the physical realizations of the de Rham cohomological operators of differential geometry. Thus, we provide a concrete proof of our earlier conjecture that any arbitrary N= 2 SUSY quantum mechanical model is an example of a Hodge theory where the cohomological operators find their physical realizations in the language of symmetry transformations of this theory. Possible physical implications of our present study are pointed out, too.

LaTeX file, 9 pages, EPJC format, To appear in EPJC

References in corpus (4)

• Self-isospectrality, special supersymmetry, and their effect on the band structure
• A field-theoretic model for Hodge theory
• One-Form Abelian Gauge Theory As The Hodge Theory
• Novel symmetries in N = 2 supersymmetric quantum mechanical models

Cited by in corpus (14)

• Novel symmetries in the modified version of two dimensional Proca theory
• Nilpotent Symmetries of a 4D Model of the Hodge Theory: Augmented (Anti-)Chiral Superfield Formalism
• General N = 2 Supersymmetric Quantum Mechanical Model: Supervariable Approach to its Off-Shell Nilpotent 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
• A Quantum Mechanical Example for Hodge 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
• Nilpotent Charges of a Toy Model of Hodge Theory and an $\mathcal{N}$ = $2$ SUSY Quantum Mechanical Model: (Anti-)Chiral Supervariable Approach
• 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
• Pseudo-Scalar Field as a Possible Candidate for Phantom Field
• Revisiting Novel Symmetries in Coupled $\mathcal{N}=2$ Supersymmetric Quantum Systems: Examples and Supervariable Approach