Abstract
This Chapter describes violation of classical symmetries by quantum effects. The aim here is to demonstrate how different types of anomalies are calculated by using spectral functions. The Chapter starts with formulation of the Noether theorems and derivation of Noether currents in a number of important examples with gauge and space-time symmetries. The following anomalies are derived by using the zeta-function techniques: axial anomaly, Einstein and Lorentz anomalies, conformal anomaly, and parity anomaly. For pedagogical purposes all calculations are done straightforwardly for two- or three-dimensional models and take into account all relevant terms which are sometime missing in original scientific papers. The results of this Chapter are also used to get with the help of anomalous transformations non-local effective actions in gravitational and gauge backgrounds, including important cases of the Polyakov-Liouville action and the Chern-Simons actions.
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Fursaev, D., Vassilevich, D. (2011). Quantum Anomalies. In: Operators, Geometry and Quanta. Theoretical and Mathematical Physics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0205-9_8
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