Christ–Lee Model: (Anti-)chiral Supervariable Approach to BRST Formalism

Abstract

We derive the off-shell nilpotent of order two and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST, and (anti-)co-BRST symmetry transformations for the Christ–Lee (CL) model in one $\left(0+1\right)$ -dimension (1D) of spacetime by exploiting the (anti-)chiral supervariable approach (ACSA) to BRST formalism where the quantum symmetry (i.e., (anti-)BRST along with (anti-)co-BRST) invariant quantities play a crucial role. We prove the nilpotency and absolute anticommutativity properties of the (anti-)BRST along with (anti-)co-BRST conserved charges within the scope of ACSA to BRST formalism where we take only one Grassmannian variable into account. We also show the (anti-)BRST and (anti-)co-BRST invariances of the Lagrangian within the scope of ACSA.