Quantization of Gauge Systems

by Marc Henneaux, Claudio Teitelboim

Overview

This book is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical foundations of BRST theory are then laid out with a review of the necessary concepts from homological algebra. Reducible gauge systems are discussed, and the relationship between BRST cohomology and gauge invariance is carefully explained. The authors then proceed to the canonical quantization of gauge systems, first without ghosts (reduced phase space quantization, Dirac method) and second in the BRST context (quantum BRST cohomology). The path integral is discussed next. The analysis covers indefinite metric systems, operator insertions, and Ward identities. The antifield formalism is also studied and its equivalence with canonical methods is derived. The examples of electromagnetism and abelian 2-form gauge fields are treated in detail.


The book gives a general and unified treatment of the subject in a self-contained manner. Exercises are provided at the end of each chapter, and pedagogical examples are covered in the text.

Product Details

ISBN-13:	9780691213866
Publisher:	Princeton University Press
Publication date:	06/16/2020
Sold by:	Barnes & Noble
Format:	eBook
Pages:	552
File size:	26 MB
Note:	This product may take a few minutes to download.

About the Author

Marc Henneaux is Maître de Recherches at the Belgian National Foundation for Scientific Research and Lecturer at the University of Brussels. Claudio Teitelboim is Director of the Centro de Estudios Cientificos de Santiago in Chile, a Professor at the University of Chile, and a Long-term Member of the Institute for Advanced Study in Princeton.

Table of Contents

Preface

Acknowledgments

Notations

Ch. 1 Constrained Hamiltonian Systems

Ch. 2 Geometry of the Constraint Surface

Ch. 3 Gauge Invariance of the Action

Ch. 4 Generally Covariant Systems

Ch. 5 First-Class Constraints: Further Developments

Ch. 6 Fermi Degrees of Freedom: Classical Mechanics over a Grassmann Algebra

Ch. 7 Constrained Systems with Fermi Variables

Ch. 8 Graded Differential Algebras - Algebraic Structure of the BRST Symmetry

Ch. 9 BRST Construction in the Irreducible Case

Ch. 10 BRST Construction in the Reducible Case

Ch. 11 Dynamics of the Ghosts - Gauge-Fixed Action

Ch. 12 The BRST Transformation in Field Theory

Ch. 13 Quantum Mechanics of Constrained Systems: Standard Operator Methods

Ch. 14 BRST Operator Method - Quantum BRST Cohomology

Ch. 15 Path Integral for Unconstrained Systems

Ch. 16 Path Integral for Constrained Systems

Ch. 17 Antifield Formalism: Classical Theory

Ch. 18 Antifield Formalism and Path Integral

Ch. 19 Free Maxwell Theory. Abelian Two-Form Gauge Field

Ch. 20 Complementary Material

Bibliography

Index

Editorial Reviews

"A useful reference for those interested in the formal aspects of constrained (i.e. gauge invariant) systems."

Physics World

"A useful reference for those interested in the formal aspects of constrained (i.e. gauge invariant) systems."—Physics World

From the Publisher