Quantization of Gauge Systems

Marc Henneaux, Claudio Teitelboim

• Publisher: Princeton University Press
• Year: 2020
• Print ISBN:
  9780691037691
  9780691087757
• eBook ISBN:
  9780691213866
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

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.

Table of contents

• Cover Page
• Half-title Page
• Title Page
• Copyright Page
• Contents
• Preface
• Acknowledgments
• Notations
• Chapter One: Constrained Hamiltonian Systems
• Chapter Two: Geometry of the Constraint Surface
• Chapter Three: Gauge Invariance of the Action
• Chapter Four: Generally Covariant Systems
• Chapter Five: First-Class Constraints: Further Developments
• Chapter Six: Fermi Degrees of Freedom: Classical Mechanics over a Grassmann Algebra
• Chapter Seven: Constrained Systems with Fermi Variables
• Chapter Eight: Graded Differential Algebras—Algebraic Structure of the BRST Symmetry
• Chapter Nine: BRST Construction in the Irreducible Case
• Chapter Ten: BRST Construction in the Reducible Case
• Chapter Eleven: Dynamics of the Ghosts—Gauge-Fixed Action
• Chapter Twelve: The BRST Transformation in Field Theory
• Chapter Thirteen: Quantum Mechanics of Constrained Systems: Standard Operator Methods
• Chapter Fourteen: BRST Operator Method—Quantum BRST Cohomology
• Chapter Fifteen: Path Integral for Unconstrained Systems
• Chapter Sixteen: Path Integral for Constrained Systems
• Chapter Seventeen: Antifleld Formalism: Classical Theory
• Chapter Eighteen: Antifield Formalism and Path Integral
• Chapter Nineteen: Free Maxwell Theory. Abelian Two-Form Gauge Field
• Chapter Twenty: Complementary Material
• Bibliography
• Index