Quantization of Gauge Systems
Princeton University Press (Verlag)
978-0-691-03769-1 (ISBN)
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.
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.
PrefaceAcknowledgmentsNotationsCh. 1Constrained Hamiltonian Systems3Ch. 2Geometry of the Constraint Surface48Ch. 3Gauge Invariance of the Action65Ch. 4Generally Covariant Systems102Ch. 5First-Class Constraints: Further Developments112Ch. 6Fermi Degrees of Freedom: Classical Mechanics over a Grassmann Algebra134Ch. 7Constrained Systems with Fermi Variables156Ch. 8Graded Differential Algebras - Algebraic Structure of the BRST Symmetry165Ch. 9BRST Construction in the Irreducible Case187Ch. 10BRST Construction in the Reducible Case205Ch. 11Dynamics of the Ghosts - Gauge-Fixed Action234Ch. 12The BRST Transformation in Field Theory253Ch. 13Quantum Mechanics of Constrained Systems: Standard Operator Methods272Ch. 14BRST Operator Method - Quantum BRST Cohomology296Ch. 15Path Integral for Unconstrained Systems333Ch. 16Path Integral for Constrained Systems380Ch. 17Antifield Formalism: Classical Theory407Ch. 18Antifield Formalism and Path Integral428Ch. 19Free Maxwell Theory. Abelian Two-Form Gauge Field455Ch. 20Complementary Material481Bibliography503Index515
| Erscheint lt. Verlag | 28.8.1994 |
|---|---|
| Zusatzinfo | 4 illus. |
| Verlagsort | New Jersey |
| Sprache | englisch |
| Maße | 197 x 254 mm |
| Gewicht | 794 g |
| Themenwelt | Naturwissenschaften ► Physik / Astronomie ► Mechanik |
| Naturwissenschaften ► Physik / Astronomie ► Quantenphysik | |
| ISBN-10 | 0-691-03769-8 / 0691037698 |
| ISBN-13 | 978-0-691-03769-1 / 9780691037691 |
| Zustand | Neuware |
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