Softcover ISBN:  9781470452711 
Product Code:  ULECT/72 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $48.00 
Electronic ISBN:  9781470453688 
Product Code:  ULECT/72.E 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $48.00 

Book DetailsUniversity Lecture SeriesVolume: 72; 2019; 192 ppMSC: Primary 81; Secondary 58; 53;
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 finitedimensional models for gauge systems and path integrals, while giving comments on what has to be amended in the infinitedimensional 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 3manifolds 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.
ReadershipGraduate students and researchers interested in mathematical aspects of quantum field theory.

Table of Contents

Chapters

Introduction

Classical Chern–Simons theory

Feynman diagrams

Batalin–Vilkovisky formalism

Applications


Additional Material

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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 finitedimensional models for gauge systems and path integrals, while giving comments on what has to be amended in the infinitedimensional 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 3manifolds 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.

Chapters

Introduction

Classical Chern–Simons theory

Feynman diagrams

Batalin–Vilkovisky formalism

Applications