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

Séré, Eric; Esteban, Maria J.; Barbaroux, Jean-Marie

Séré, Eric; Esteban, Maria J.; Barbaroux, Jean-Marie (2005), Some connections between Dirac-Fock and Electron-Positron Hartree-Fock, Annales Henri Poincaré, 6, 1, p. 85-102. http://dx.doi.org/10.1007/s00023-005-0199-7

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00012913/en/

Date

2005

Journal name

Annales Henri Poincaré

Volume

Number

Pages

85-102

Abstract (EN)

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.

Subjects / Keywords

Mathematics; Mathematical Physics; Physics; Quantum Algebra