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1 Genesis of quantum anomalies; 2 The Feynman path integral and Schwinger’s action principle; 3 Quantum theory of photons and the phase operator; 4 Regularization of field theory and chiral anomalies; 5 The Jacobian in path integrals and quantum anomalies; 6 Quantum breaking of gauge symmetry; 7 The Weyl anomaly and renormalization group; 8 Two-dimensional field theory and bosonization; 9 Index theorem on the lattice and chiral anomalies; 10 Gravitational anomalies; 11 Concluding remarks; A Basics of quantum electrodynamics; B Field theory in curved space-time; C References with brief comments

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