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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.
List of contents
| Preface | |
| Acknowledgments | |
| Notations | |
| Ch. 1 | Constrained Hamiltonian Systems | 3 |
| Ch. 2 | Geometry of the Constraint Surface | 48 |
| Ch. 3 | Gauge Invariance of the Action | 65 |
| Ch. 4 | Generally Covariant Systems | 102 |
| Ch. 5 | First-Class Constraints: Further Developments | 112 |
| Ch. 6 | Fermi Degrees of Freedom: Classical Mechanics over a Grassmann Algebra | 134 |
| Ch. 7 | Constrained Systems with Fermi Variables | 156 |
| Ch. 8 | Graded Differential Algebras - Algebraic Structure of the BRST Symmetry | 165 |
| Ch. 9 | BRST Construction in the Irreducible Case | 187 |
| Ch. 10 | BRST Construction in the Reducible Case | 205 |
| Ch. 11 | Dynamics of the Ghosts - Gauge-Fixed Action | 234 |
| Ch. 12 | The BRST Transformation in Field Theory | 253 |
| Ch. 13 | Quantum Mechanics of Constrained Systems: Standard Operator Methods | 272 |
| Ch. 14 | BRST Operator Method - Quantum BRST Cohomology | 296 |
| Ch. 15 | Path Integral for Unconstrained Systems | 333 |
| Ch. 16 | Path Integral for Constrained Systems | 380 |
| Ch. 17 | Antifield Formalism: Classical Theory | 407 |
| Ch. 18 | Antifield Formalism and Path Integral | 428 |
| Ch. 19 | Free Maxwell Theory. Abelian Two-Form Gauge Field | 455 |
| Ch. 20 | Complementary Material | 481 |
| Bibliography | 503 |
| Index | 515 |
About the author
Marc Henneaux & Claudio Teitelboim
Summary
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.
Additional text
"A useful reference for those interested in the formal aspects of constrained (i.e. gauge invariant) systems."
