## Anomalies in quantum field theoryAn 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. |

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### Contents

Introduction | 1 |

Differential geometry topology and fibre | 10 |

Path integrals FP method and | 118 |

Copyright | |

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### Common terms and phrases

Abelian Alvarez-Gaume amplitude analogous axial current boundary calculate chain of descent chain term Chern-Simons form chiral cohomology commutator consider coordinate corresponds covariant anomaly covariant derivative curvature defined Definition denotes descent equations determinant differential forms dimensions Dirac operator Einstein exterior derivative fermion fibre bundle field theory formula FP ghost Fujikawa gauge element gauge fields gauge group gauge invariant gauge potential gauge theory gauge transformation geometric Ginsparg Grassmann gravitational anomaly Green functions homotopy index theorem infinitesimal invariant polynomial Jacobian Lagrangian Lemma Lie algebra Lie derivative Lie G loop Lorentz manifold matrix metric non-Abelian anomaly obtain p-form path integral principal bundle Proposition quantum action recall equation recall Section regularization relation represents scalar singlet anomaly spinor Stora symmetry tensor topological space TP(M transition functions trivial vanishes variation vector field vielbein Ward identity wedge product Weyl winding number WZ consistency condition YM field Zumino