FLPR Model: (Anti-)Chiral Supervariable Approach to Quantum Symmetries

TL;DR

This paper develops a supervariable approach to derive and prove the properties of BRST and co-BRST symmetries in a 1D quantum model, providing a novel geometric framework for understanding these symmetries.

Contribution

It introduces an anti-chiral supervariable method to systematically derive and analyze nilpotent and anti-commuting BRST and co-BRST symmetries for the FLPR model.

Findings

Derived off-shell nilpotent BRST and co-BRST transformations.

Proved nilpotency and anti-commutativity of conserved charges.

Showed invariance of the Lagrangian under these symmetries.

Abstract

We discuss and derive the off-shell nilpotent of order two and absolutely anti-commuting Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST, co-BRST and anti-co-BRST symmetry transformations for the non-interacting Friedberg-Lee-Pang-Ren (FLPR) model in one (0 + 1)-dimension (1D) of spacetime by exploiting the standard techniques of the (anti-)chiral supervariable approach (ACSA) onto (1, 1)-dimensional super sub-manifold of the general (1, 2)-dimensional supermanifold, where the (anti-)BRST and (anti-)co-BRST invariant restrictions play a crucial role. We provide clear proof of nilpotency and absolute anti-commutativity properties of the (anti-)BRST as well as (anti-)co-BRST Noether's conserved charges within the framework of ACSA to BRST formalism, where we take only one Grassmannian variable in place of two usual Grassmannian variables (i.e., fermionic variables). Furthermore, we also demonstrate that the Lagrangian of this non-interacting FLPR model is (anti-)BRST as well as (anti-)co-BRST symmetries invariance within the ambit of the ACSA to BRST approach in (1, 1)-dimensional super sub-manifold.