Reparameterization Invariant Model of a Supersymmetric System: BRST and Supervariable Approaches

TL;DR

This paper develops a BRST quantization framework for a supersymmetric 1D relativistic particle model using supervariable approaches, revealing new invariance properties and restrictions that are universal across similar models.

Contribution

It introduces the application of modified Bonora-Tonin supervariable approach and (anti-)chiral supervariable approach to a SUSY system, deriving novel BRST symmetries and CF-type restrictions.

Findings

Derivation of nilpotent (anti-)BRST transformations for target variables.

Proof of the CF-type restriction's invariance and universality.

Establishment of absolute anticommutativity of BRST charges.

Abstract

We carry out the Becchi-Rouet-Stora-Tyutin (BRST) quantization of the one (0 + 1)-dimensional (1D) model of a free massive spinning relativistic particle (i.e. a supersymmetric system) by exploiting its classical infinitesimal and continuous reparameterization symmetry transformations. We use the modified Bonora-Tonin (BT) supervariable approach (MBTSA) to BRST formalism to obtain the nilpotent (anti-)BRST symmetry transformations of the target space variables and the (anti-)BRST invariant Curci-Ferrari (CF)-type restriction for the 1D model of our supersymmetric (SUSY) system. The nilpotent (anti-)BRST symmetry transformations for other variables of our model are derived by using the (anti-)chiral supervariable approach (ACSA) to BRST formalism. Within the framework of the latter, we have shown the existence of the CF-type restriction by proving the (i) symmetry invariance of the coupled Lagrangians, and (ii) the absolute anticommutativity property of the conserved (anti-)BRST charges. The application of the MBTSA to a physical SUSY system (i.e. a 1D model of a massive spinning particle) is a novel result in our present endeavor. In the application of ACSA, we have considered only the (anti-)chiral super expansions of the supervariables. Hence, the observation of the absolute anticommutativity of the (anti-)BRST charges is a novel result. The CF-type restriction is universal in nature as it turns out to be the same for the SUSY and non-SUSY reparameterization (i.e. 1D diffeomorphism) invariant models of the (non-)relativistic particles.