New Forms of BRST Symmetry on a Prototypical First-Class System

TL;DR

This paper explores various known and new forms of BRST symmetries within a prototypical first-class system, revealing their interrelations, underlying group structures, and implications for quantum field theory.

Contribution

It introduces new forms of BRST symmetries, including a generalized set and a novel unprecedented set, and analyzes their connections and roles in gauge-invariant systems.

Findings

Identifies a $ Z_4\times\nZ_2$ symmetry group in the ghost sector.

Shows how symmetries relate via canonical transformations in Hamiltonian formalism.

Highlights the significance of dual BRST symmetries in a gauge-fixed Lagrangian context.

Abstract

We scrutinize the many known forms of BRST symmetries, as well as some new ones, realized within a prototypical first-class system. Similarities and differences among ordinary BRST, anti-BRST, dual-BRST and anti-dual-BRST symmetries are highlighted and discussed. We identify a precise $\mathbb{Z}_4\times\mathbb{Z}_2$ discrete group of symmetries of the ghost sector, responsible for connecting the various forms of BRST transformations. Considering a Hamiltonian approach, those symmetries can be interrelated by canonical transformations among ghost variables. However, the distinguished characteristic role of the dual BRST symmetries can be fully appreciated within a gauge-fixed Lagrangian viewpoint. New forms of BRST symmetries are given, a set generalizing particular ones previously reported in the literature as well as a brand new unprecedented set. The featured gauge invariant prototypical first-class system encompasses an extensive class of physical models and sheds light on previous controversies in the current quantum field theory literature.