Geometric Interpretation of the Quantum Master Equation in the BRST--anti-BRST Formalism

TL;DR

This paper extends the geometric interpretation of the antibracket formalism to include anti-BRST symmetry, enabling a supermanifold-based formulation of the quantum master equation and proving its equivalence with the standard formalism.

Contribution

It introduces a geometric framework for the BRST--anti-BRST formalism, unifying it with the existing antibracket approach through supermanifold integration theory.

Findings

Extended the geometric interpretation to anti-BRST symmetry

Formulated the quantum master equation in supermanifold terms

Proved equivalence with the standard antibracket formalism

Abstract

The geometric interpretation of the antibracket formalism given by Witten is extended to cover the anti-BRST symmetry. This enables one to formulate the quantum master equation for the BRST--anti-BRST formalism in terms of integration theory over a supermanifold. A proof of the equivalence of the standard antibracket formalism with the antibracket formalism for the BRST--anti-BRST symmetry is also given.