A Note on Gauge Transformations in Batalin-Vilkovisky Theory

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 $dμ_S = dμe^{2S/\hbar}$ 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 $dμ_S$. We discuss closed string field theory as an application.