On possible generalizations of field--antifield formalism

TL;DR

This paper proposes a generalized, coordinate-invariant extension of the field-antifield formalism, incorporating Dirac's antibrackets, hypergauge fixing, and BRST transformations, applicable to systems with constraints.

Contribution

It introduces a generalized, coordinate-invariant framework for the field-antifield formalism, including new definitions for antibrackets and hypergauge functions, and extends BRST transformations.

Findings

Coordinate-invariant quantum master equation formulated.

Hypergauge functions characterized as antisymplectic first-class constraints.

Functional integral shown to be independent of hypergauge variations.

Abstract

A generalized version is proposed for the field-antifield formalism. The antibracket operation is defined in arbitrary field-antifield coordinates. The antisymplectic definitions are given for first- and second-class constraints. In the case of second-class constraints the Dirac's antibracket operation is defined. The quantum master equation as well as the hypergauge fixing procedure are formulated in a coordinate-invariant way. The general hypergauge functions are shown to be antisymplectic first-class constraints whose Jacobian matrix determinant is constant on the constraint surface. The BRST-type generalized transformations are defined and the functional integral is shown to be independent of the hypergauge variations admitted. In the case of reduced phase space the Dirac's antibrackets are used instead of the ordinary ones.