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Title: The fermionic projector in a time-dependent external potential: Mass oscillation property and Hadamard states

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 the 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.

Authors:
; ;  [1]
  1. Fakultät für Mathematik, Universität Regensburg, D-93040 Regensburg (Germany)
Publication Date:
OSTI Identifier:
22596631
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 7; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FERMIONS; MASS; MINKOWSKI SPACE; OSCILLATIONS; POTENTIALS; QUANTUM FIELD THEORY; TIME DEPENDENCE

Citation Formats

Finster, Felix, E-mail: finster@ur.de, E-mail: simone.murro@ur.de, E-mail: Christian.Roeken@mathematik.ur.de, Murro, Simone, E-mail: finster@ur.de, E-mail: simone.murro@ur.de, E-mail: Christian.Roeken@mathematik.ur.de, and Röken, Christian, E-mail: finster@ur.de, E-mail: simone.murro@ur.de, E-mail: Christian.Roeken@mathematik.ur.de. The fermionic projector in a time-dependent external potential: Mass oscillation property and Hadamard states. United States: N. p., 2016. Web. doi:10.1063/1.4954806.
Finster, Felix, E-mail: finster@ur.de, E-mail: simone.murro@ur.de, E-mail: Christian.Roeken@mathematik.ur.de, Murro, Simone, E-mail: finster@ur.de, E-mail: simone.murro@ur.de, E-mail: Christian.Roeken@mathematik.ur.de, & Röken, Christian, E-mail: finster@ur.de, E-mail: simone.murro@ur.de, E-mail: Christian.Roeken@mathematik.ur.de. The fermionic projector in a time-dependent external potential: Mass oscillation property and Hadamard states. United States. doi:10.1063/1.4954806.
Finster, Felix, E-mail: finster@ur.de, E-mail: simone.murro@ur.de, E-mail: Christian.Roeken@mathematik.ur.de, Murro, Simone, E-mail: finster@ur.de, E-mail: simone.murro@ur.de, E-mail: Christian.Roeken@mathematik.ur.de, and Röken, Christian, E-mail: finster@ur.de, E-mail: simone.murro@ur.de, E-mail: Christian.Roeken@mathematik.ur.de. Fri . "The fermionic projector in a time-dependent external potential: Mass oscillation property and Hadamard states". United States. doi:10.1063/1.4954806.
@article{osti_22596631,
title = {The fermionic projector in a time-dependent external potential: Mass oscillation property and Hadamard states},
author = {Finster, Felix, E-mail: finster@ur.de, E-mail: simone.murro@ur.de, E-mail: Christian.Roeken@mathematik.ur.de and Murro, Simone, E-mail: finster@ur.de, E-mail: simone.murro@ur.de, E-mail: Christian.Roeken@mathematik.ur.de and Röken, Christian, E-mail: finster@ur.de, E-mail: simone.murro@ur.de, E-mail: Christian.Roeken@mathematik.ur.de},
abstractNote = {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 the 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.},
doi = {10.1063/1.4954806},
journal = {Journal of Mathematical Physics},
number = 7,
volume = 57,
place = {United States},
year = {Fri Jul 15 00:00:00 EDT 2016},
month = {Fri Jul 15 00:00:00 EDT 2016}
}