Symmetry transformations in Batalin-Vilkovisky formalism

TL;DR

This paper analyzes symmetry transformations in the Batalin-Vilkovisky formalism, establishing conditions for physical equivalence of solutions and showing how quantum observables generate symmetries.

Contribution

It provides a clear formulation of conditions for physical equivalence and demonstrates how quantum observables induce symmetries in the BV approach.

Findings

Every quantum observable determines a symmetry of the theory.

Conditions for physical equivalence of solutions are formulated.

Analysis clarifies the role of observables in symmetry transformations.

Abstract

This short note is closely related to Sen-Zwiebach paper on gauge transformations in Batalin-Vilkovisky theory (hep-th 9309027). We formulate some conditions of physical equivalence of solutions to the quantum master equation and use these conditions to give a very transparent analysis of symmetry transformations in BV-approach. We prove that in some sense every quantum observable (i.e. every even function $H$ obeying $\Delta_{\rho}(He^S)=0$) determines a symmetry of the theory with the action functional $S$ satisfying quantum master equation $\Delta_{\rho}e^S=0$ \end