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

Annales Henri Poincare

Volumn 6, Issue 1, 2005, Pages 85-102

  Barbaroux, Jean Marie ^a   Esteban, Maria J ^b   Séré, Eric ^b  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

^b UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 15244360825     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-005-0199-7     Document Type: Article

References (18)

1. B. Swirles, The relativistic self-consistent field, Proc. Roy. Soc. A 152, 625-649 (1935).
2. I. Lindgren, A. Rosen, Relativistic self-consistent field calculations, Case Stud. At. Phys. 4, 93-149 (1974).
3. O. Gorceix, P. Indelicato, J.P. Desclaux, Multiconfiguration Dirac-Fock studies of two-electron ions: I. Electron-electron interaction, J. Phys. B: At. Mol. Phys. 20, 639-649 (1987).
4. M.J. Esteban, E. Séré, Solutions for the Dirac-Fock equations for atoms and molecules, Comm. Math. Phys. 203, 499-530 (1999).
5. E. Paturel, Solutions of the Dirac equations without projector, A.H.P. 1, 1123-1157 (2000).
6. M.H. Mittleman, Theory of relativistic effects on atoms: Configuration-space Hamiltonian, Phys. Rev. A 24(3), 1167-1175 (1981).
7. J. Sucher, Foundations of the relativistic theory of many-particle atoms, Phys. Rev. A 22(2), 348-362 (1980).
8. J. Sucher, Relativistic many-electron Hamiltonians, Phys. Scrypta 36, 271-281 (1987).
9. P. Chaix, D. Iracane, From quantum electrodynamics to mean-field theory: I. The Bogoliubov-Dirac-Fock formalism, J. Phys. B 22 (23), 3791-3814 (December 1989).
10. V. Bach, J.M. Barbaroux, B. Helffer, H. Siedentop, Stability of matter for the Hartree-Fock functional of the relativistic electron-positron field, Doc. Math. 3, 353-364 (1998).
11. V. Bach, J.M. Barbaroux, B. Helffer, H. Siedentop, On the stability of the relativistic electron-positron field, Comm. Math. Phys. 201(2), 445-460 (1999).
12. J.-M. Barbaroux, W. Farkas, B. Helffer, H. Siedentop, On the Hartree-Fock equations of the electron-positron field, Preprint.
13. P. Chaix, D. Iracane, P.L. Lions, From quantum electrodynamics to mean-field theory: II. Variational stability of the vacuum of quantum electrodynamics in the mean-field approximation, J. Phys. B 22 (23), 3815-3828 (December 1989).
14. M.J. Esteban, E. Séré, Nonrelativistic limit of the Dirac-Fock equations, A.H.P. 2, 941-961 (2001).
15. M.J. Esteban, E. Séré, A max-min principle for the ground state of the Dirac-Fock functional, Contemp. Mathem. 307, 135-139 (2002).
16. B. Thaller, The Dirac Equation, Springer-Verlag, 1992.
17. V. Bach, E.H. Lieb, M. Loss, J.P. Solovej, There are no unfilled shells in unrestricted Hartree-Fock theory, Phys. Rev. Lett. 72(19), 2981-2983 (1994).
18. A. Ambrosetti, M. Badiale, Homoclinics: Poincaré-Melnikov type results via a variational approach, Annales de l'IHP, Analyse non linéaire 15(2), 233-252 (1998).