An introduction to the Batalin-Vilkovisky formalism

TL;DR

This paper introduces the Batalin-Vilkovisky formalism, focusing on the quantum and classical master equations, their connections to Lie algebra representations, and perturbative Gaussian integrals, within finite-dimensional examples.

Contribution

It provides an accessible introduction to the BV formalism, highlighting its relations to BRST theory and perturbative methods in a finite-dimensional setting.

Findings

Relation between quantum master equation and Lie algebra representations

Connection of classical master equation with BRST formalism

Illustration of concepts through finite-dimensional examples

Abstract

The aim of these notes is to introduce the quantum master equation $\{S,S\}-2i\hbar\Delta S=0$, 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.