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

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

2004-02-21

arxiv.org/abs/math-ph/0402058v3

Physics

Mathematical Physics

Scientific paper

10.1007/s00023-005-0199-7

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.

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