Some connections between Dirac-Fock and electron-positron Hartree-Fock

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 minmax problem. Then we investigate a max-min problem coming from the electronpositron field theory of Bach-Barbaroux-Helffer-Siedentop. We show that given a radially symmetric nuclear charge, the ground state of Dirac-Fock solves this maxmin 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. © Birkhäuser Verlag, Basel, 2005.