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_μS≡d_μe^(2S/ħ) invariant. The quantum gauge transformations and their Lie algebra are ħ-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_μS. We discuss closed string field theory as an application.