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

January 22, 2015

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.

open access link
doi:10.1063/1.4954806

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@article{Finster:2015wga,
author = "Finster, Felix and Murro, Simone and Röken, Christian",
title = "{The Fermionic Projector in a Time-Dependent External
Potential: Mass Oscillation Property and Hadamard States}",
journal = "J. Math. Phys.",
volume = "57",
year = "2016",
number = "7",
pages = "072303",
doi = "10.1063/1.4954806",
eprint = "1501.05522",
archivePrefix = "arXiv",
primaryClass = "math-ph",
SLACcitation = "%%CITATION = ARXIV:1501.05522;%%"
}

Keywords:

Hadamard states, Mass oscillation property, Fermionic Signature Operator, massive Dirac equation