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A Rigorous Geometric Derivation of the Chiral Anomaly in Curved Backgrounds
- We discuss the chiral anomaly for a Weyl field in a curved background and show that a novel index theorem for the Lorentzian Dirac operator can be applied to describe the gravitational chiral anomaly. A formula for the total charge generated by the gravitational and gauge field background is derived directly in Lorentzian signature and in a mathematically rigorous manner. It contains a term identical to the integrand in the Atiyah-Singer index theorem and another term involving the.-invariant of the Cauchy hypersurfaces.
Author details: | Christian BärORCiDGND, Alexander Strohmaier |
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DOI: | https://doi.org/10.1007/s00220-016-2664-1 |
ISSN: | 0010-3616 |
ISSN: | 1432-0916 |
Title of parent work (English): | Communications in mathematical physics |
Publisher: | Springer |
Place of publishing: | New York |
Publication type: | Article |
Language: | English |
Year of first publication: | 2016 |
Publication year: | 2016 |
Release date: | 2020/03/22 |
Volume: | 347 |
Number of pages: | 19 |
First page: | 703 |
Last Page: | 721 |
Funding institution: | Deutsche Forschungsgemeinschaft [Sonderforschungshereich 647]; ESI |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |