The Fermionic Signature Operator in De Sitter Spacetime

Claudio Dappiaggi, Felix Finster, Simone Murro, Emanuela Radici
February 25, 2019
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.
open access link
@article{Dappiaggi:2019oew, author = "Dappiaggi, Claudio and Finster, Felix and Murro, Simone and Radici, Emanuela", title = "{The Fermionic Signature Operator in De Sitter Spacetime}", year = "2019", eprint = "1902.09144", archivePrefix = "arXiv", primaryClass = "math-ph", SLACcitation = "%%CITATION = ARXIV:1902.09144;%%" }

Keywords: 
Hadamard states, Ferminic Signature Operator, Dirac operator, de Sitter spacetime