Calculus of Variations and Geometric Measure Theory

C. Dappiaggi - F. Finster - S. Murro - E. Radici

The Fermionic Signature Operator in De Sitter Spacetime

created by radici on 10 Apr 2020
modified on 28 Oct 2022


Published Paper

Inserted: 10 apr 2020
Last Updated: 28 oct 2022

Journal: Journal of Mathematical Analysis and Applications
Year: 2020

ArXiv: 1902.09144 PDF


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.