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.
Inhaltsverzeichnis
<TR>Preface<TR>Acknowledgments<TR>Notations<TR>Ch. 1Constrained Hamiltonian Systems3<TR>Ch. 2Geometry of the Constraint Surface48<TR>Ch. 3Gauge Invariance of the Action65<TR>Ch. 4Generally Covariant Systems102<TR>Ch. 5First-Class Constraints: Further Developments112<TR>Ch. 6Fermi Degrees of Freedom: Classical Mechanics over a Grassmann Algebra134<TR>Ch. 7Constrained Systems with Fermi Variables156<TR>Ch. 8Graded Differential Algebras - Algebraic Structure of the BRST Symmetry165<TR>Ch. 9BRST Construction in the Irreducible Case187<TR>Ch. 10BRST Construction in the Reducible Case205<TR>Ch. 11Dynamics of the Ghosts - Gauge-Fixed Action234<TR>Ch. 12The BRST Transformation in Field Theory253<TR>Ch. 13Quantum Mechanics of Constrained Systems: Standard Operator Methods272<TR>Ch. 14BRST Operator Method - Quantum BRST Cohomology296<TR>Ch. 15Path Integral for Unconstrained Systems333<TR>Ch. 16Path Integral for Constrained Systems380<TR>Ch. 17Antifield Formalism: Classical Theory407<TR>Ch. 18Antifield Formalism and Path Integral428<TR>Ch. 19Free Maxwell Theory. Abelian Two-Form Gauge Field455<TR>Ch. 20Complementary Material481<TR>Bibliography503<TR>Index515
