A Free N = 2 Supersymmetric System: Novel Symmetries

Abstract

We discuss a set of novel discrete symmetries of a free N = 2 supersymmetric (SUSY) quantum mechanical system which is the limiting case of a widely-studied interacting SUSY model of a charged particle constrained to move on a sphere in the background of a Dirac magnetic monopole. The usual continuous symmetries of this model provide the physical realization of the de Rham cohomological operators of differential geometry. The interplay between the novel discrete symmetries and usual continuous symmetries leads to the physical realization of relationship between the (co-)exterior derivatives of differential geometry. We have also exploited the supervariable approach to derive the nilpotent N = 2 SUSY symmetries of the theory and provided the geometrical origin and interpretation for the nilpotency property. Ultimately, our present study (based on innate symmetries) proves that our free N = 2 SUSY example is a tractable model for the Hodge theory.

arXiv commentLaTeX file, 12 pages, Journal reference is given

References in corpus (18)

• Supersymmetry and Quantum Mechanics
• Duality, Self-Duality, Sources and Charge Quantization in Abelian N-Form Theories
• New Supersymmetry of the Monopole
• New topological field theories in two dimensions
• A field-theoretic model for Hodge theory
• New local symmetry for QED in two dimensions
• Rigid Rotor as a Toy Model for Hodge Theory
• Abelian p-Form (p = 1, 2, 3) Gauge Theories as the Field Theoretic Models for the Hodge Theory
• One-Form Abelian Gauge Theory As The Hodge Theory
• On free 4D Abelian 2-form and anomalous 2D Abelian 1-form gauge theories
• Novel symmetries in the modified version of two dimensional Proca theory
• Dual-BRST symmetry: 6D Abelian 3-form gauge theory
• Supersymmetric Oscillator: Novel Symmetries
• Novel symmetries in N = 2 supersymmetric quantum mechanical models
• General N = 2 Supersymmetric Quantum Mechanical Model: Supervariable Approach to its Off-Shell Nilpotent Symmetries
• Supersymmetric Monopole Quantum Mechanics on Sphere
• N=4 Supersymmetric Quantum Mechanics with Magnetic Monopole
• Comments on the dual-BRST symmetry

Cited by in corpus (12)

• Modified 2D Proca Theory: Revisited Under BRST and (Anti-)Chiral Superfield Formalisms
• (Anti-)chiral Superfield Approach to Nilpotent Symmetries: Self-Dual Chiral Bosonic Theory
• (Anti-)Chiral Superfield Approach to Interacting Abelian 1-Form Gauge Theories: Nilpotent and Absolutely Anticommuting Charges
• (Anti-)Chiral Supervariable Approach to Nilpotent and Absolutely Anticommuting Conserved Charges of Reparameterization Invariant Theories: A Couple of Relativistic Toy Models as Examples
• A Quantum Mechanical Example for Hodge Theory
• Novel symmetries in an interacting N = 2 supersymmetric quantum mechanical model
• Massive 4D Abelian 2-Form Theory: Nilpotent Symmetries from the (Anti-)Chiral Superfield Approach
• Christ-Lee Model: (Anti-)Chiral Supervariable Approach to BRST Formalism
• Nilpotent Charges in an Interacting Gauge Theory and an N = 2 SUSY Quantum Mechanical Model: (Anti-)Chiral Superfield Approach
• 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