The Fermionic Projector in a Time-Dependent External Potential: Mass Oscillation Property and Hadamard States

TL;DR

This paper constructs a non-perturbative fermionic projector in Minkowski space with a time-dependent external potential, proving key properties and establishing a Hadamard state for quantum field theory.

Contribution

It introduces a novel non-perturbative approach to the fermionic projector in time-dependent external potentials, demonstrating mass oscillation properties and Hadamard form.

Findings

Proves weak and strong mass oscillation properties.

Shows the fermionic projector's kernel is of Hadamard form under certain conditions.

Establishes a quantum field theory framework with a distinguished Hadamard state.

Abstract

We give a non-perturbative construction of the fermionic projector in Minkowski space coupled to a time-dependent external potential which is smooth and decays faster than quadratically for large times. The weak and strong mass oscillation properties are proven. We show that the integral kernel of the fermionic projector is of Hadamard form, provided that the time integral of the spatial sup-norm of the potential satisfies a suitable bound. This gives rise to an algebraic quantum field theory of Dirac fields in an external potential with a distinguished pure quasi-free Hadamard state.