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

TL;DR

This paper develops a supervariable approach to derive and prove the properties of BRST, anti-BRST, co-BRST, and anti-co-BRST symmetries for the Christ-Lee model in 1D, ensuring their nilpotency and anti-commutativity.

Contribution

It introduces an anti-chiral supervariable method to systematically derive and verify the (anti-)BRST and (anti-)co-BRST symmetries for the Christ-Lee model, highlighting their invariance and algebraic properties.

Findings

Derived off-shell nilpotent and anti-commuting (anti-)BRST and (anti-)co-BRST transformations.

Proved nilpotency and anti-commutativity of the conserved charges within the supervariable framework.

Established invariance of the Lagrangian under these symmetries.

Abstract

We derive the off-shell nilpotent of order two and absolutely anti-commuting Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and (anti-)co-BRST symmetry transformations for the Christ--Lee (CL) model in one (0 + 1)-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 anti-commutativity 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.