SEMICLASSICAL APPROXIMATION IN BATALIN-VILKOVISKY FORMALISM

The geometry of supermanifolds provided with a Q-structure (i.e. with an odd vector field Q satisfying {Q, Q} = 0), a P-structure (odd symplectic structure) and an S-structure (volume element) or with various combinations of these structures is studied. The results are applied to the analysis of the Batalin-Vilkovisky approach to the quantization of gauge theories. In particular the semiclassical approximation in this approach is expressed in terms of Reidemeister torsion.