Anomalies in Quantum Field Theory

An anomaly is the failure of a classical symmetry to survive the process of quantization and regularization. The study of anomalies has played an important role in quantum field theory in the last 20 years, one which is described clearly and comprehensively in this book, the first textbook on the subject. The author approaches the subject through differential geometry, a method that has received much attention in recent years, and gives detailed derivations and calculations which will be invaluable to both students and researchers in theoretical and mathematical physics.

An anomaly 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 20 years. This text 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 as an aid to students. 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. The comprehensive overview of the theory presented in this book will be useful to both students and researchers.

1 - Introduction
2 - Differential geometry, topology and fibre bundles
3 - Path integrals, FP method and BRS transformation
4 - Anomalies in QFT
5 - Path integral and anomaly
6 - Physics in terms of differential forms
7 - Chern-Simons form, homotopy operator and anomaly
8 - Consistent anomaly
9 - Stora-Zumino chain of descent equations
10 - Covariant anomaly
11 - Index and anomaly
12 - Gravitation

Dr R.A. Bertlmann, Professor of Physics, Institute of Theoretical Physics, University of Vienna, Austria.