Anomalies in Quantum Field Theory

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.

It is essentially self-contained and thus deserves to be called a textbook. Both mathematicians and physicists can learn from this volume. * CERN Courier * A comprehensive monograph on anomalies has long been missing - Bertlmann's book thus represents a highly desirable filling of the gap ... Bertlmann's book can be warmly recommended to Ph.D. students, lecturers and researchers working in the quantum field theory and mathematical physics, since its contents are unique within the existing literature and cover, in an essential way, the development of modern methods in this area. * EMS *

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