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

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Date
2005
Link to item file
http://hal.archives-ouvertes.fr/hal-00012913/en/
Dewey
Probabilités et mathématiques appliquées
Sujet
Mathematics; Mathematical Physics; Physics; Quantum Algebra
Journal issue
Annales Henri Poincaré
Volume
6
Number
1
Publication date
2005
Article pages
85-102
DOI
http://dx.doi.org/10.1007/s00023-005-0199-7
URI
https://basepub.dauphine.fr/handle/123456789/385
Collections
  • CEREMADE : Publications
Metadata
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Author
Séré, Eric
Esteban, Maria J.
Barbaroux, Jean-Marie
Type
Article accepté pour publication ou publié
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.

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