Lectures on Batalin-Vilkovisky formalism and its applications in topological quantum field theory

TL;DR

This paper provides an accessible introduction to the Batalin-Vilkovisky formalism and its applications in topological quantum field theory, focusing on the mathematical aspects of gauge theories and perturbative path integrals.

Contribution

It offers a comprehensive, pedagogical overview of the Batalin-Vilkovisky formalism tailored for a mathematical audience, emphasizing its role in topological quantum field theory.

Findings

Clarifies the mathematical structure of the BV formalism

Connects BV formalism with topological quantum field theories

Provides foundational insights for further research in gauge theories

Abstract

Lecture notes for the course "Batalin-Vilkovisky formalism and applications in topological quantum field theory" given at the University of Notre Dame in the Fall 2016 for a mathematical audience. In these lectures we give a slow introduction to the perturbative path integral for gauge theories in Batalin-Vilkovisky formalism and the associated mathematical concepts.