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

Long Meng (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Keywords: Dirac--Fock model; electron-positron Hatree--Fock model; Mittleman's conjecture; ground state energy

Domains: Mathematics [math]; Analysis of PDEs [math.AP]; Mathematics [math]; Mathematical Physics [math-ph]; Physics [physics]; Quantum Physics [quant-ph]

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