The Fermionic Signature Operator in De Sitter Spacetime

Abstract

The fermionic projector state is a distinguished quasi-free state for the algebra of Dirac fields in a globally hyperbolic spacetime. We construct and analyze it in the four-dimensional de Sitter spacetime, both in the closed and in the flat slicing. In the latter case we show that the mass oscillation properties do not hold due to boundary effects. This is taken into account in a so-called mass decomposition. The involved fermionic signature operator defines a fermionic projector state. In the case of a closed slicing, we construct the fermionic signature operator and show that the ensuing state is maximally symmetric and of Hadamard form, thus coinciding with the counterpart for spinors of the Bunch-Davies state.

28 pages - accepted in Journal of Mathematical Analysis and Applications

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• Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds
• On the Cauchy problem for Friedrichs systems on globally hyperbolic manifolds with timelike boundary
• The Fermionic Signature Operator in the Exterior Schwarzschild Geometry
• A Canonical Complex Structure and the Bosonic Signature Operator for Scalar Fields in Globally Hyperbolic Spacetimes
• Integrability of Dirac equations in static spherical space-times
• A comparison of the Georgescu and Vasy spaces associated to the N-body problems and applications
• On the uniqueness of invariant states