An introduction to the Batalin-Vilkovisky formalism

Abstract

The aim of these notes is to introduce the quantum master equation $\{S,S\}-2i\hbarΔS=0$, and to show its relations to the theory of Lie algebras representations and to perturbative expansions of Gaussian integrals. The relations of the classical master equation $\{S,S\}=0$ with the BRST formalisms are also described. Being an introduction, only finite-dimensional examples will be considered.

19 pages. Lecture given at the "Rencontres Mathematiques de Glanon", July 2003. Final version. Minor corrections