Existence of global-in-time solutions to a generalized Dirac-Fock type evolution equation
Abstract
We consider a generalized Dirac-Fock type evolution equation deduced from no-photon Quantum Electrodynamics, which describes the self-consistent time-evolution of relativistic electrons, the observable ones as well as those filling up the Dirac sea. This equation has been originally introduced by Dirac in 1934 in a simplified form. Since we work in a Hartree-Fock type approximation, the elements describing the physical state of the electrons are infinite rank projectors. Using the Bogoliubov-Dirac-Fock formalism, introduced by Chaix-Iracane ({\it J. Phys. B.}, 22, 3791--3814, 1989), and recently established by Hainzl-Lewin-Sere, we prove the existence of global-in-time solutions of the considered evolution equation.
Keywords
Cite
@article{arxiv.math-ph/0412018,
title = {Existence of global-in-time solutions to a generalized Dirac-Fock type evolution equation},
author = {Christian Hainzl and Mathieu Lewin and Christof Sparber},
journal= {arXiv preprint arXiv:math-ph/0412018},
year = {2009}
}
Comments
12 pages; more explanations added, some final (minor) corrections included