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A Gutzwiller type trace formula for the magnetic Dirac operator

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Abstract

For manifolds including metric-contact manifolds with non-resonant Reeb flow, we prove a Gutzwiller type trace formula for the associated magnetic Dirac operator involving contributions from Reeb orbits on the base. As an application, we prove a semiclassical limit formula for the eta invariant.

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Acknowledgements

The author would like to thank the anonymous referee for a careful reading and several constructive suggestions and improvements.

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Authors and Affiliations

  1. Laboratoire Jacques Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC), 4 place Jussieu, 75252, Paris Cedex 05, France

    Nikhil Savale

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  1. Nikhil Savale
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Correspondence to Nikhil Savale.

Additional information

The author acknowledges the financial support of the Agence Nationale de la Recherche, Project ANR-15-CE40-0018 (Sub-Riemannian Geometry and Interactions).

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Savale, N. A Gutzwiller type trace formula for the magnetic Dirac operator. Geom. Funct. Anal. 28, 1420–1486 (2018). https://doi.org/10.1007/s00039-018-0462-y

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  • DOI: https://doi.org/10.1007/s00039-018-0462-y

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