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

Abstract

We perform the Becchi-Rouet-Stora-Tyutin (BRST) quantization of the one (0 + 1)-dimensional (1D) model of a 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 derive the off-shell 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 where the CF-type restriction appears in the proof of (i) the invariance of the coupled (but equivalent) Lagrangians, and (ii) the absolute anticommutativity of the conserved and off-shell nilpotent (anti-)BRST charges. The application of the MBTSA to a physical SUSY system (i.e. 1D model of a massive spinning particle) is a novel result in our present endeavor. The proof of the absolute anticommutativity of the conserved (anti-)BRST charges (within the framework of ACSA) is another very interesting observation in view of the fact that only the (anti-)chiral super expansions of the supervariables have been taken into account.The CF-type restriction is universal in nature as it turns out to be the same for the SUSY and non-SUSY reparameterizaion (i.e. 1D diffeomorphism) invariant theories.