Forms of BRST symmetry on a Prototypical First-Class System

TL;DR

This paper explores different forms of BRST symmetry in a prototypical first-class system using the Batalin-Fradkin-Vilkovisky formalism, highlighting how canonical transformations reveal these symmetries.

Contribution

It demonstrates that various BRST symmetries, including dual-BRST, can be derived from the standard BRST symmetry through canonical transformations in the ghost sector.

Findings

Dual-BRST symmetry is obtained from usual BRST via canonical transformation.

Different forms of BRST symmetry are systematically derived.

The formalism clarifies the geometric roots of these symmetries.

Abstract

We obtain the various forms of BRST symmetry by using the Batalin-Fradkin-Vilkovisky formalism in a prototypical first class system. We have shown that the various forms of symmetry can be obtained through canonical transformation in the ghost sector. The so called "dual-BRST" symmetry which is claimed to be an independent symmetry due to its roots in differential geometry is obtained from usual BRST symmetry by making a canonical transformation in the ghost sector.