An index theorem on asymptotically static spacetimes with compact Cauchy surface
| Autor: | Dawei Shen, Michał Wrochna |
|---|---|
| Přispěvatelé: | Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Université de Cergy Pontoise (UCP), Université Paris-Seine |
| Rok vydání: | 2021 |
| Předmět: | |
| DOI: | 10.48550/arxiv.2104.02816 |
| Popis: | We consider the Dirac operator on asymptotically static Lorentzian manifolds with an odd-dimensional compact Cauchy surface. We prove that if Atiyah-Patodi-Singer boundary conditions are imposed at infinite times then the Dirac operator is Fredholm. This generalizes a theorem due to B\"ar-Strohmaier in the case of finite times, and we also show that the corresponding index formula extends to the infinite setting. Furthermore, we demonstrate the existence of a Fredholm inverse which is at the same time a Feynman parametrix in the sense of Duistermaat-H\"ormander. The proof combines methods from time-dependent scattering theory with a variant of Egorov's theorem for pseudo-differential hyperbolic systems. Comment: 41 pages; v3: minor fixes, references added, accepted in Pure Appl. Anal |
| Databáze: | OpenAIRE |
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