Nilpotent Symmetries For A Free Relativistic Particle In Augmented Superfield Formalism

TL;DR

This paper derives nilpotent (anti-)BRST symmetry transformations for a free relativistic particle using augmented superfield formalism, providing geometric insights and a prototype for reparametrization invariant theories.

Contribution

It introduces a novel application of augmented superfield formalism to derive nilpotent symmetries for a relativistic particle, linking geometry with physical symmetries.

Findings

Derived off-shell nilpotent (anti-)BRST transformations.

Provided geometric interpretation of charges.

Established a prototype for string and gravitational theories.

Abstract

In the framework of the augmented superfield formalism, the local, covariant, continuous and off-shell (as well as on-shell) nilpotent (anti-)BRST symmetry transformations are derived for a $(0 + 1)$-dimensional free scalar relativistic particle that provides a prototype physical example for the more general reparametrization invariant string- and gravitational theories. The trajectory (i.e. the world-line) of the free particle, parametrized by a monotonically increasing evolution parameter $\tau$, is embedded in a $D$-dimensional flat Minkowski target manifold. This one-dimensional system is considered on a $(1 + 2)$-dimensional supermanifold parametrized by an even element $\tau$ and a couple of odd elements ($\theta$ and $\bar\theta$) of a Grassmannian algebra. The horizontality condition and the invariance of the conserved (super)charges on the (super)manifolds play very crucial roles in the above derivations of the nilpotent symmetries. The geometrical interpretations for the nilpotent (anti-)BRST charges are provided in the framework of augmented superfield approach.