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Geometry and Theoretical Physics pp 178–209Cite as

Anomalies in Quantum Field Theory

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Abstract

A review is presented of the anomaly problem in quantum field theory. The problems encountered in evaluating the π0 → 2γ decay are described, as well as the point-splitting method for dealing with these problems and deriving the chiral anomaly. We next show how the Wess-Zumino consistency conditions allow the understanding of these results in the context of the cohomology of Lie algebras. Then some concepts from the theory of characteristic classes are discussed, including the Chern character, in order to derive the descent equations which are the basis for the algebraic calculation of anomalies. Finally, the relation of the anomaly problem to the question of Schwinger terms in current algebra is clarified.

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Author information

Authors and Affiliations

  1. Institut für Physik der Universität, P.O. Box 500 500, D(W)-4600, Dortmund 50, Federal Republic of Germany

    Allen C. Hirshfeld

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  1. Allen C. Hirshfeld
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Editors and Affiliations

  1. Physikzentrum Bad Honnef, Hauptstraße 5, W-5340, Bad Honnef, Fed. Rep. of Germany

    Joachim Debrus

  2. Lehrstuhl für Theoretische Physik III, Universität Dortmund, Postfach 500500, W-4600, Dortmund 1, Fed. Rep. of Germany

    Allen C. Hirshfeld

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© 1991 Springer-Verlag Berlin Heidelberg

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Hirshfeld, A.C. (1991). Anomalies in Quantum Field Theory. In: Debrus, J., Hirshfeld, A.C. (eds) Geometry and Theoretical Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76353-3_6

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  • DOI: https://doi.org/10.1007/978-3-642-76353-3_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-76355-7

  • Online ISBN: 978-3-642-76353-3

  • eBook Packages: Springer Book Archive

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