PATH INTEGRAL AND QUANTUM ANOMALIES   by Kazuo Fujikawa February 2001, 210 x 148 mm, 300pp., 6,600- Quantum anomalies correspond to the breaking of certain symmetry properties by the quantization procedure in field theory. The initial indication of quantum anomaly was recognized immediately after the birth of modern quantum theory, namely, renormalization theory, but its true physical significance was fully recognized only in 1969. Since then, quantum anomalies have become one of the most profound and important notions of modern field theory. Quantum anomalies played prominent roles not only in the establishment of the Standard Model of elementary particles, but also in the recent development in string theory. At this moment, quantum anomalies are classified into two basic categories, chiral anomaly and Weyl (or conformal) anomaly. In this monograph, a path integral approach to quantum anomalies, which was initiated by the author and developed later by the efforts of many people, is presented in a coherent manner. In the path integral approach, all the known quantum anomalies are identified as non-trivial Jacobian factors under the relevant symmetry transformations of path integral variables. This approach provides a unified view of the symmetry breaking phenomena by quantization procedure itself. It also provides a transparent picture for the topological aspects of quantum anomalies, which are related to the Atiyah-Singer index theorem and the Riemann-Roch theorem. Path integral approach also proved to be useful recently in the treatment of chiral anomaly in lattice gauge theory and the bosonization of Abelian and non-Abelian models in two-dimensional theory. A coherent treatment of the path integral method is presented in this book starting with an elementary account of Feynman path integral and Schwinger's action principle. This book is aimed to be accessible to readers with a basic knowledge of quantum theory at the level of beginning graduate students. Contents Chapter 1: Birth of renormalization theory and the discovery of quantum anomaly Chapter 2: Feynman path integral and Schwinger's action principle Chapter 3: Quantum theory of light and the photon phase operator Chapter 4: Regularization of field theory and chiral anomaly Chapter 5: Jacobian in path integral and quantum anomalies Chapter 6: Non-Abelian gauge anomalies Chapter 7: Weyl anomaly and renormalization group Chapter 8: Gravitational anomalies Chapter 9: Index theorem and chiral anomaly in lattice gauge theory Chapter 10: Two-dimensional field theory and bosonization Chapter 11: Closing remarks Appendices A. Brief summary of quantum electrodynamics B. Brief account of field theory in curved space-time C. References with brief comments About the Author Born in 1942. MS, Department of Physics, University of Tokyo. Ph.D, Princeton University in 1970. Presently Professor in Department of Physics, University of Tokyo. His contributions to field theory include the formulation of Rξ-gauge in spontaneously broken gauge theory (with B.W. Lee and A.I. Sanda) besides the path integral formulation of quantum anomalies. Received Nishina Memorial Prize in 1986.