# The Fermionic Signature Operator in De Sitter Spacetime

## TL;DR

This paper constructs and analyzes the fermionic signature operator in four-dimensional de Sitter spacetime, demonstrating its properties and relation to known states like the Bunch-Davies state, with implications for quantum field theory in curved spacetime.

## Contribution

It introduces the fermionic signature operator in de Sitter spacetime and shows it yields a maximally symmetric Hadamard state, extending the understanding of fermionic states in curved backgrounds.

## Key findings

- The fermionic signature operator defines a maximally symmetric Hadamard state.
- In flat slicing, boundary effects prevent mass oscillation properties, requiring a mass decomposition.
- The constructed state coincides with the Bunch-Davies state in the closed slicing.

## 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.