Renormalization and asymptotic expansion of Dirac's polarized vacuum

Philippe Gravejat (1, 2) , Mathieu Lewin (3) , Eric Séré (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 DMA - Département de Mathématiques et Applications - ENS Paris
3 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

We perform rigorously the charge renormalization of the so-called reduced Bogoliubov-Dirac-Fock (rBDF) model. This nonlinear theory, based on the Dirac operator, describes atoms and molecules while taking into account vacuum polarization effects. We consider the total physical density including both the external density of a nucleus and the self-consistent polarization of the Dirac sea, but no 'real' electron. We show that it admits an asymptotic expansion to any order in powers of the physical coupling constant $\alphaph$, provided that the ultraviolet cut-off behaves as $\Lambda\sim e^{3\pi(1-Z_3)/2\alphaph}\gg1$. The renormalization parameter $0

Mots clés: Charge renormalization; Quantum Electrodynamics; vacuum polarization; Dirac sea; Uehling potential; Bogoliubov-Dirac-Fock model; Relativistic Density Functional Theory

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Philippe Gravejat, Mathieu Lewin, Eric Séré. Renormalization and asymptotic expansion of Dirac's polarized vacuum. Communications in Mathematical Physics, 2011, 306 (1), pp.1-33. ⟨10.1007/s00220-011-1271-4⟩. ⟨hal-00472276⟩