Annales Henri Poincaré

, Volume 6, Issue 1, pp 85–102

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


    • CPT-CNRS
  • Maria J. Esteban
    • Ceremade (UMR CNRS no. 7534)Université Paris IX-Dauphine
  • Eric Séré
    • Ceremade (UMR CNRS no. 7534)Université Paris IX-Dauphine
Original Paper

DOI: 10.1007/s00023-005-0199-7

Cite this article as:
Barbaroux, J., Esteban, M.J. & Séré, E. Ann. Henri Poincaré (2005) 6: 85. doi: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 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.

Copyright information

© Birkhäuser Verlag, Basel 2005