Bertlmann R.A. Anomalies in Quantum Field Theory

Clarendon Press, 1996. - 566 pp.
The anomaly, which forms the central part of this book, is the failure of classical symmetry to survive the process of quantization and regularization. The study of anomalies is the key to a deeper understanding of quantum field theory and has played an increasingly important role in the theory over the past twenty years. This book presents all the different aspects of the study of anomalies in an accessible and self-contained way. Much emphasis is now being placed on the formulation of the theory using the mathematical ideas of differential geometry and topology. This approach is followed here, and the derivations and calculations are given explicitly. Topics discussed include the relevant ideas from differential geometry and topology and the application of these paths (path integrals, differential forms, homotopy operators, etc.) to the study of anomalies. Chapters are devoted to abelian and nonabelian anomalies, consistent and covariant anomalies, and gravitational anomalies.Differential geometry, topology and fibre bundles.
Path integrals, FP method and BRS transformation.
Anomalies in QFT.
Path integral and anomaly.
Physics in terms of differential forms.
Chern–Simons form, homotopy operator and anomaly.
Consistent anomaly.
Stora–Zumino chain of descent equations.
Covariant anomaly.
Index and anomaly.
Gravitation.