Symmetries and the Antibracket

TL;DR

This paper develops a generalized BRST formalism using the antibracket and introduces a new Grassmann-odd bracket, providing a unified framework for deriving identities in gauge theories.

Contribution

It introduces a new Grassmann-odd bracket that generalizes the antibracket and demonstrates its application within the BRST formalism for gauge theories.

Findings

A new Grassmann-odd bracket reduces to the conventional antibracket in a special limit.

The formalism unifies various identities in gauge theories under a common BRST framework.

Illustrative examples demonstrate the applicability of the generalized formalism.

Abstract

Requiring that a Lagrangian path integral leads to certain identities (Ward identities in a broad sense) can be formulated in a general BRST language, if necessary by the use of collective fields. The condition of BRST symmetry can then be expressed with the help of the antibracket, and suitable generalizations thereof. In particular, a new Grassmann-odd bracket, which reduces to the conventional antibracket in a special limit, naturally appears. We illustrate the formalism with various examples.