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Local index theory for Lorentzian manifolds

By Christian Bär

Appears in collection : Geometry and analysis on non-compact manifolds / Géométrie et analyse sur les variétés non compactes

We prove a local version of the index theorem for Dirac-type operators on globally hyperbolic Lorentzian manifolds with Cauchy boundary. In case the Cauchy hypersurface is compact, we do not assume self-adjointness of the Dirac operator on the spacetime or of the associated elliptic Dirac operator on the boundary.In this case, integration of our local index theorem results in a generalization of previously known index theorems for globally hyperbolic spacetimes that allows for twisting bundles associated with non-compact gauge groups. This is joint work with Alexander Strohmaier.

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Citation data

  • DOI 10.24350/CIRM.V.19902003
  • Cite this video Bär Christian (3/29/22). Local index theory for Lorentzian manifolds. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19902003
  • URL https://dx.doi.org/10.24350/CIRM.V.19902003


  • BÄR, Christian et STROHMAIER, Alexander. A rigorous geometric derivation of the chiral anomaly in curved backgrounds. Communications in Mathematical Physics, 2016, vol. 347, no 3, p. 703-721. - https://doi.org/10.1007/s00220-016-2664-1
  • BÄR, Christian et STROHMAIER, Alexander. An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary. American Journal of Mathematics, 2019, vol. 141, no 5, p. 1421-1455. - https://doi.org/10.1353/ajm.2019.0037
  • BÄR, Christian et STROHMAIER, Alexander. Local index theory for Lorentzian manifolds. arXiv preprint arXiv:2012.01364, 2020. - https://arxiv.org/abs/2012.01364

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