Quantum Field Theory: Batalin–Vilkovisky Formalism and Its Applications
About this Title
Pavel Mnev, Steklov Institute of Mathematics, St. Petersburg, Russia
Publication: University Lecture Series
Publication Year: 2019; Volume 72
ISBNs: 978-1-4704-5271-1 (print); 978-1-4704-5368-8 (online)
MathSciNet review: 3967709
MSC: Primary 81S40; Secondary 57R56, 81T13, 81T45
This book originated from lecture notes for the course given by the author at the University of Notre Dame in the fall of 2016. The aim of the book is to give an introduction to the perturbative path integral for gauge theories (in particular, topological field theories) in Batalin–Vilkovisky formalism and to some of its applications. The book is oriented toward a graduate mathematical audience and does not require any prior physics background. To elucidate the picture, the exposition is mostly focused on finite-dimensional models for gauge systems and path integrals, while giving comments on what has to be amended in the infinite-dimensional case relevant to local field theory. Motivating examples discussed in the book include Alexandrov–Kontsevich–Schwarz–Zaboronsky sigma models, the perturbative expansion for Chern–Simons invariants of 3-manifolds given in terms of integrals over configurations of points on the manifold, the BF theory on cellular decompositions of manifolds, and Kontsevich's deformation quantization formula.
Graduate students and researchers interested in mathematical aspects of quantum field theory.
Table of Contents
- Classical Chern–Simons theory
- Feynman diagrams
- Batalin–Vilkovisky formalism