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

Long Meng
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#### Abstract

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 $\alpha$ is small and the velocity of light $c$ is large. As a byproduct, we also prove, when $\alpha$ 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.

### Dates and versions

hal-03928154 , version 1 (06-01-2023)

### Identifiers

• HAL Id : hal-03928154 , version 1
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### Cite

Long Meng. A rigorous justification of the Mittleman's approach to the Dirac--Fock model. 2023. ⟨hal-03928154⟩

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