Semiclassical approximation in Batalin-Vilkovisky formalism

TL;DR

This paper explores the geometric structures of supermanifolds with various algebraic structures and applies these findings to the Batalin-Vilkovisky quantization method, linking semiclassical approximation to Reidemeister torsion.

Contribution

It provides a geometric framework for the Batalin-Vilkovisky formalism and expresses the semiclassical approximation using Reidemeister torsion.

Findings

Geometric analysis of supermanifolds with Q, P, and S structures

Application of geometric structures to BV quantization

Semiclassical approximation expressed via Reidemeister torsion

Abstract

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