English

Some connections between Dirac-Fock and Electron-Positron Hartree-Fock

Mathematical Physics 2009-11-10 v3 math.MP

Abstract

We study the ground state solutions of the Dirac-Fock model in the case of weak electronic repulsion, using bifurcation theory. They are solutions of a min-max problem. Then we investigate a max-min problem coming from the electron-positron field theory of Bach-Barbaroux-Helffer-Siedentop. We show that given a radially symmetric nuclear charge, the ground state of Dirac-Fock solves this max-min problem for certain numbers of electrons. But we also exhibit a situation in which the max-min level does not correspond to a solution of the Dirac-Fock equations together with its associated self-consistent projector.

Keywords

Cite

@article{arxiv.math-ph/0402058,
  title  = {Some connections between Dirac-Fock and Electron-Positron Hartree-Fock},
  author = {Jean-Marie Barbaroux and Maria J. Esteban and Eric Séré},
  journal= {arXiv preprint arXiv:math-ph/0402058},
  year   = {2009}
}