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 $d\hat{I}{¼}_S=d\hat{I}¼e^{2S/\hslash }$ invariant. The quantum gauge transformations and their Lie algebra are $\hslash$-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 $d\hat{I}{¼}_S$. We discuss closed string field theory as an application.

10 pages, phyzzx.tex, MIT-CTP-2240