Path Integrals and Quantum Anomalies

Paperback | December 21, 2013

byKazuo Fujikawa, Hiroshi Suzuki

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The Feynman path integrals are becoming increasingly important in the applications of quantum mechanics and field theory. The path integral formulation of quantum anomalies, i.e. the quantum breaking of certain symmetries, can now cover all the known quantum anomalies in a coherent manner. Inthis book the authors provide an introduction to the path integral method in quantum field theory and its applications to the analyses of quantum anomalies. No previous knowledge of field theory beyond advanced undergraduate quantum mechanics is assumed. The book provides the first coherent introductory treatment of the path integral formulation of chiral and Weyl anomalies, with applications to gauge theory in two and four dimensions, conformal field theory and string theory. Explicit and elementary path integral calculations of most of the quantumanomalies covered are given. The conceptual basis of the path integral bosonization in two-dimensional theory, which may have applications to condensed matter theory, for example, is clarified. The book also covers the recent interesting developments in the treatment of fermions and chiral anomaliesin lattice gauge theory.

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The Feynman path integrals are becoming increasingly important in the applications of quantum mechanics and field theory. The path integral formulation of quantum anomalies, i.e. the quantum breaking of certain symmetries, can now cover all the known quantum anomalies in a coherent manner. Inthis book the authors provide an introductio...

Kazuo Fujikawa is in the Department of Physics at the University of Tokyo in Japan. Hiroshi Suzuki is in the Department of Mathematical Sciences at Ibaraki University in Japan.

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Format:PaperbackDimensions:296 pages, 9.21 × 6.14 × 0.01 inPublished:December 21, 2013Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:019968670X

ISBN - 13:9780199686704

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Table of Contents

1. Genesis of quantum anomalies2. The Feynman path integral and Schwinger's action principle3. Quantum theory of photons and the phase operator4. Regularization of field theory and chiral anomalies5. The Jacobian in path integrals and quantum anomalies6. Quantum breaking of gauge symmetry7. The Weyl anomaly and renormalization group8. Two-dimensional field theory and bosonization9. Index theorem on the lattice and chiral anomalies10. Gravitational anomalies11. Concluding remarksA. Basics of quantum electrodynamicsB. Field theory in curved space-timeC. References with brief comments

Editorial Reviews

"An excellent addition to the literature by one of the pioneers in understanding anomalies." --Roman Jackiw, Massachusetts Institute of Technology