Publication Date:
2011-06-10
Description:
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 ρ ph including both the external density of a nucleus and the self-consistent polarization of the Dirac sea, but no ‘real’ electron. We show that ρ ph admits an asymptotic expansion to any order in powers of the physical coupling constant α ph , provided that the ultraviolet cut-off behaves as L ~ e 3 p (1 - Z 3 )/2 a ph 〉〉 1 . The renormalization parameter 0 〈 Z 3 〈 1 is defined by Z 3 = α ph / α , where α is the bare coupling constant. The coefficients of the expansion of ρ ph are independent of Z 3 , as expected. The first order term gives rise to the well-known Uehling potential, whereas the higher order terms satisfy an explicit recursion relation. Content Type Journal Article Pages 1-33 DOI 10.1007/s00220-011-1271-4 Authors Philippe Gravejat, Centre de Mathématiques Laurent Schwartz (UMR 7640), École Polytechnique, 91128 Palaiseau Cedex, France Mathieu Lewin, CNRS & Laboratoire de Mathématiques (UMR 8088), Université de Cergy-Pontoise, 95000 Cergy-Pontoise, France Éric Séré, Ceremade (UMR 7534), Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France Journal Communications in Mathematical Physics Online ISSN 1432-0916 Print ISSN 0010-3616
Print ISSN:
0010-3616
Electronic ISSN:
1432-0916
Topics:
Mathematics
,
Physics
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