Nilpotent Symmetries For A Spinning Relativistic Particle In Augmented Superfield Formalism

TL;DR

This paper derives and geometrically interprets nilpotent BRST and anti-BRST symmetries for a spinning relativistic particle using an augmented superfield formalism on a supermanifold.

Contribution

It introduces a novel augmented superfield approach to obtain and interpret BRST symmetries for a (0+1)-dimensional spinning particle.

Findings

Derived two sets of (anti-)BRST symmetry transformations.

Provided geometric interpretations of the symmetries.

Applied the formalism to a physically relevant one-dimensional system.

Abstract

The local, covariant, continuous, anticommuting and nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for all the fields of a (0 + 1)-dimensional spinning relativistic particle are obtained in the framework of augmented superfield approach to BRST formalism. The trajectory of this super-particle is parametrized by a monotonically increasing parameter \tau that is embedded in a D-dimensional flat Minkowski spacetime manifold. This physically useful one-dimensional system is considered on a three (1 + 2)-dimensional supermanifold which is parametrized by an even element \tau and a couple of odd elements \theta and \bar\theta of the Grassmann algebra. Two anticommuting sets of (anti-)BRST symmetry transformations, corresponding to the underlying (super)gauge symmetries for the above system, are derived in the framework of augmented superfield formulation where (i) the horizontality condition, and (ii) the invariance of conserved quantities on the supermanifold, play decisive roles. Geometrical interpretations for the above nilpotent symmetries (and their generators) are provided.