A new class of Fermionic Projectors: M{\o}ller operators and mass oscillation properties

TL;DR

This paper explores a new class of Fermionic Projectors using M{\

Contribution

It introduces a modified construction of quasi-free states for the self-dual CAR algebra that relaxes the strong mass oscillation property requirement.

Findings

Identifies a scenario where the strong mass oscillation property fails due to nonvanishing trace on the Rindler horizon.

Proposes a modified construction that weakens the original condition.

Establishes a connection between the original and modified approaches.

Abstract

Recently, a new functional analytic construction of quasi-free states for a self-dual CAR algebra has been presented in \cite{Felix2}. This method relies on the so-called strong mass oscillation property. We provide an example where this requirement is not satisfied, due to the nonvanishing trace of the solutions of the Dirac equation on the horizon of Rindler space, and we propose a modification of the construction in order to weaken this condition. Finally, a connection between the two approaches is built.