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≡ dμ exp (2S/ ) ̵ invariant. The quantum gauge transformations and their Lie algebra are - ̵ 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 μ s . We discuss closed string field theory as an application.