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

TL;DR

This paper develops a supervariable approach to derive and analyze (anti-)BRST symmetries and charges in reparameterization invariant toy models of relativistic particles, revealing their absolute anticommutativity and nilpotency.

Contribution

It introduces a novel (anti-)chiral supervariable method to obtain (anti-)BRST symmetries, demonstrating absolute anticommutativity of charges without requiring Curci-Ferrari restrictions for scalar particles.

Findings

(Anti-)BRST charges are absolutely anticommuting.

Nilpotency of conserved charges is established.

(Anti-)BRST invariance of Lagrangians is demonstrated.

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.