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Geometry and Physics: Volume IA Festschrift in honour of Nigel Hitchin$
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Andrew Dancer, Jørgen Ellegaard Andersen, and Oscar García-Prada

Print publication date: 2018

Print ISBN-13: 9780198802013

Published to Oxford Scholarship Online: December 2018

DOI: 10.1093/oso/9780198802013.001.0001

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Boundary Value Problems for the Lorentzian Dirac Operator

Boundary Value Problems for the Lorentzian Dirac Operator

(p.3) 1 Boundary Value Problems for the Lorentzian Dirac Operator
Geometry and Physics: Volume I

Christian Bär

Sebastian Hannes

Oxford University Press

On a compact globally hyperbolic Lorentzian spin manifold with smooth space-like Cauchy boundary, the (hyperbolic) Dirac operator is known to be Fredholm when Atiyah–Patodi–Singer boundary conditions are imposed. This chapter explores to what extent these boundary conditions can be replaced by more general ones and how the index then changes. There are some differences to the classical case of the elliptic Dirac operator on a Riemannian manifold with boundary.

Keywords:   globally hyperbolic, Dirac operator, index theorem, boundary value problem, Fredholm operator

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