FLPR Model: Nilpotent (Anti-)co-BRST Symmetries

TL;DR

This paper introduces a new set of off-shell nilpotent and anticommuting (anti-)co-BRST symmetry transformations in the BRST formalism for the FLPR model, revealing novel symmetries that preserve the gauge-fixing term.

Contribution

The work identifies and formulates a novel set of fermionic (anti-)co-BRST symmetries beyond the standard (anti-)BRST symmetries in the FLPR model, expanding the understanding of gauge symmetries.

Findings

Derived conserved, off-shell nilpotent (anti-)BRST and (anti-)co-BRST charges.

Established the physicality criteria and operator form of first-class constraints.

Demonstrated the invariance of the gauge-fixing term under (anti-)co-BRST transformations.

Abstract

We demonstrate the existence of a set of novel off-shell nilpotent and absolutely anticommuting continuous symmetry transformations, within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism, which are over and above the usual off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetry transformations that are respected by the first-order Lagrangian for the Friedberg-Lee-Pang-Ren (FLPR) model that describes the motion of a non-relativistic particle of unit mass moving under the influence of a general rotationally invariant spatial two-dimensional potential. We christen these novel set of fermionic symmetry transformations as the (anti-)co-BRST symmetry transformations because the gauge-fixing term remains invariant under them. We derive the conserved and off-shell nilpotent (anti-)BRST and (anti-)co-BRST charges and comment on the physicality criteria w.r.t. them where we establish the presence of the operator forms of the first-class constraints (of the original classical gauge theory) at the quantum level.