Anomalies and Schwinger Terms in NCG Field Theory Models

  1. Dr. Dietrich Papenfuß2,
  2. Professor Dr. Dieter Lüst3 and
  3. Professor Dr. Wolfgang P. Schleich4
  1. Jouko A. Mickelsson

Published Online: 29 NOV 2007

DOI: 10.1002/9783527610853.ch41

100 Years Werner Heisenberg: Works and Impact

100 Years Werner Heisenberg: Works and Impact

How to Cite

Mickelsson, J. A. (2002) Anomalies and Schwinger Terms in NCG Field Theory Models, in 100 Years Werner Heisenberg: Works and Impact (eds D. Papenfuß, D. Lüst and W. P. Schleich), Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527610853.ch41

Editor Information

  1. 2

    Alexander von Humboldt-Stiftung, Bonn, Germany

  2. 3

    Humboldt Universität, Institut für Physik, Germany

  3. 4

    Universität Ulm, Abteilung f. Quantenphysik, Albert-Einstein-Allee 11, 89069 Ulm, Germany

Author Information

  1. Mathematical Physics, Royal Institute of Technology, SCFAB, SE-10691, Stockholm, Sweden

Publication History

  1. Published Online: 29 NOV 2007
  2. Published Print: 27 AUG 2002

ISBN Information

Print ISBN: 9783527403929

Online ISBN: 9783527610853

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Keywords:

  • quantum field theory;
  • gravitation;
  • anomalies;
  • Schwinger terms;
  • NCG field theory models;
  • quantization of chiral fermions;
  • generalized Dirac operators;
  • NCG Yang-Mills theory

Summary

This talk is based on the paper [1], which contains references to the original literature. We study the quantization of chiral fermions coupled to generalized Dirac operators arising in NCG Yang-Mills theory. The cocycles describing chiral symmetry breaking are calculated. In particular, we introduce a generalized locality principle for the cocycles. Local cocycles are by definition expressions which can be written as generalized traces of operator commutators. In the case of pseudodifferential operators, these traces lead in fact to integrals of ordinary local de Rham forms. As an application of the general ideas we take the case of noncommutative tori.