Bär, C. and Strohmaier, A. orcid.org/0000-0002-8446-3840 (2024) Local index theory for Lorentzian manifolds. Annales Scientifiques de l’École Normale Supérieure, 57 (6). pp. 1693-1752. ISSN 0012-9593
Abstract
Index theory for Lorentzian Dirac operators is a young subject with significant differences to elliptic index theory. It is based on microlocal analysis instead of standard elliptic theory and one of the main features is that a nontrivial index is caused by topologically nontrivial dynamics rather than nontrivial topology of the base manifold. In this paper we establish a local index formula for Lorentzian Dirac-type operators on globally hyperbolic spacetimes. This local formula implies an index theorem for general Dirac-type operators on spatially compact spacetimes with Atiyah-Patodi-Singer boundary conditions on Cauchy hypersurfaces. This is significantly more general than the previously known theorems that require the compatibility of the connection with Clifford multiplication and the spatial Dirac operator on the Cauchy hypersurface to be selfadjoint with respect to a positive definite inner product.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This item is protected by copyright. This is an author produced version of an article published in Annales Scientifiques de l’École Normale Supérieure. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Dirac-type operator, globally hyperbolic Lorentzian manifold, Atiyah-Patodi-Singer boundary conditions, Feynman propagator, local index theorem, Hadamard expansion |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 31 Jul 2023 13:54 |
Last Modified: | 21 Feb 2025 10:08 |
Published Version: | https://smf.emath.fr/publications/theorie-locale-d... |
Status: | Published |
Publisher: | Société Mathematique de France |
Identification Number: | 10.24033/asens.2597 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:201959 |