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A rigorous justification of the Mittleman's approach to the Dirac--Fock model

Meng, Long (2023), A rigorous justification of the Mittleman's approach to the Dirac--Fock model. https://basepub.dauphine.psl.eu/handle/123456789/24495

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Type
Document de travail / Working paper
Date
2023
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
20
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Author(s)
Meng, Long
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
In this paper, we study the relationship between the Dirac--Fock model and the electron-positron Hartree--Fock model. We justify the Dirac--Fock model as a variational approximation of QED when the vacuum polarization is neglected and when the fine structure constant α is small and the velocity of light c is large. As a byproduct, we also prove, when α is small or c is large, the no-unfilled shells theory in the Dirac--Fock theory for atoms and molecules. The proof is based on some new properties of the Dirac--Fock model.
Subjects / Keywords
Dirac--Fock model; electron-positron Hatree--Fock model; Mittleman's conjecture; ground state energy