Massive Spinning Relativistic Particle: Revisited Under BRST and Supervariable Approaches

TL;DR

This paper revisits the gauge and BRST symmetries of a 1D massive spinning relativistic particle using supervariable approaches, deriving new results on charge properties and restrictions.

Contribution

It introduces the anti-chiral supervariable approach to derive BRST symmetries and the Curci-Ferrari restriction for the first time in this context.

Findings

Derived nilpotent BRST and anti-BRST charges.

Established the Curci-Ferrari restriction via symmetry invariance.

Proved absolute anticommutativity of charges using only (anti-)chiral super expansions.

Abstract

We discuss the continuous and infinitesimal gauge, supergauge, reparameterization, nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetries and derive corresponding nilpotent charges for the one (0+1)-dimensional (1D) massive model of a spinning relativistic particle. We exploit the theoretical potential and power of the BRST and supervariable approaches to derive the (anti-)BRST symmetries and coupled (but equivalent) Lagrangians for this system. In particular, we capture the off-shell nilpotency and absolute anticommutatvity of the conserved (anti-)BRST charges within the framework of the newly proposed (anti-)chiral supervariable approach (ACSA) to BRST formalism where only the (anti-)chiral supervariables (and their suitable super expansions are taken into account along the Grassmannian direction(s)). One of the novel observations of our present investigation is the derivation of the Curci-Ferrari (CF)-type restriction by the requirement of the absolute anticommutatvity of the (anti-)BRST charges in the ordinary space. We obtain the same restriction within the framework of ACSA to BRST formalism by (i) the symmetry invariance of the coupled Lagrangians, and (ii) the proof of the absolute anticommutatvity of the conserved and nilpotent (anti-)BRST charges. The observation of the anticommutativity property of the (anti-)BRST charges is a novel result in view of the fact that we have taken into account only the (anti-)chiral super expansions.