The Fermionic Signature Operator and Hadamard States in the Presence of a Plane Electromagnetic Wave

TL;DR

This paper constructs a special quantum state for the Dirac field in Minkowski space with a plane electromagnetic wave, demonstrating it is a Hadamard state through explicit fermionic signature operator computation.

Contribution

It provides a non-perturbative method to construct Hadamard states for the Dirac field in the presence of a plane electromagnetic wave, including explicit operator analysis.

Findings

Dirac operator exhibits strong mass oscillation property

Fermionic projector state is proven to be Hadamard

Explicit computation of the fermionic signature operator

Abstract

We give a non-perturbative construction of a distinguished state for the quantized Dirac field in Minkowski space in the presence of a time-dependent external field of the form of a plane electromagnetic wave. By explicit computation of the fermionic signature operator, it is shown that the Dirac operator has the strong mass oscillation property. We prove that the resulting fermionic projector state is a Hadamard state.