(Anti-)Chiral Supervariable Approach to Nilpotent and Absolutely Anticommuting Conserved Charges of Reparameterization Invariant Theories: A Couple of Relativistic Toy Models as Examples

Abstract

We exploit the potential and power of the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST invariant restrictions on the (anti-)chiral supervariables to derive the proper (anti-)BRST symmetries for the reparameterization invariant one (0+1)-dimensional (1D) toy models of the free relativistic particle as well as free spinning (i.e. supersymmetric) relativistic particle within the framework of (anti-)chiral supervariable approach to BRST formalism. Despite the (anti-)chiral super expansions of the (anti-)chiral supervariables, we observe that the (anti-)BRST charges, for the above toy models, turn out to be absolutely anticommuting in nature. This is one of the novel observations of our present endeavor. For this proof, we utilize the beauty and strength of Curci-Ferrari (CF) type restriction in the case of spinning relativistic particle but no such restriction is required in the case of the free scalar relativistic particle. We have also captured the nilpotency property of the conserved charges as well as the (anti-)BRST invariance of the appropriate Lagrangian(s) of our present toy models within the framework of (anti-)chiral supervariable approach.

arXiv commentLaTeX file, 32 pages, journal version

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Cited by in corpus (6)

• Modified 2D Proca Theory: Revisited Under BRST and (Anti-)Chiral Superfield Formalisms
• Christ-Lee Model: (Anti-)Chiral Supervariable Approach to BRST Formalism
• Massive 4D Abelian 2-Form Theory: Nilpotent Symmetries from the (Anti-)Chiral Superfield Approach
• 1D Diffeomorphism Invariant Model of a Free Scalar Relativistic Particle: Supervariable and BRST Approaches
• Massive Spinning Relativistic Particle: Revisited Under BRST and Supervariable Approaches
• Nilpotent Charges in an Interacting Gauge Theory and an N = 2 SUSY Quantum Mechanical Model: (Anti-)Chiral Superfield Approach