A Note on Gauge Transformations in Batalin-Vilkovisky Theory

TL;DR

This paper provides a covariant symplectic geometric framework for understanding gauge transformations in Batalin-Vilkovisky quantization, extending classical concepts to the quantum level with applications to string field theory.

Contribution

It introduces a symplectic geometric description of gauge transformations at both classical and quantum levels within BV theory, including their algebraic structures and measure invariance.

Findings

Quantum gauge transformations are $ ext{h}$-deformations of classical ones.

The Lie brackets are constructed in terms of symplectic structure and measure.

Application to closed string field theory demonstrates the framework's relevance.

Abstract

We give a generally covariant description, in the sense of symplectic geometry, of gauge transformations in Batalin-Vilkovisky quantization. Gauge transformations exist not only at the classical level, but also at the quantum level, where they leave the action-weighted measure $d\mu_S = d\mu e^{2S/\hbar}$ invariant. The quantum gauge transformations and their Lie algebra are $\hbar$-deformations of the classical gauge transformation and their Lie algebra. The corresponding Lie brackets $[ , ]^q$, and $[ , ]^c$, are constructed in terms of the symplectic structure and the measure $d\mu_S$. We discuss closed string field theory as an application.