Charge renormalisation in a mean-field approximation of QED
Sok, Jérémy (2014), Charge renormalisation in a mean-field approximation of QED. https://basepub.dauphine.fr/handle/123456789/13305
TypeDocument de travail / Working paper
External document linkhttp://hal.archives-ouvertes.fr/hal-00909168
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Abstract (EN)We study the Bogoliubov-Dirac-Fock (BDF) model, a no-photon, mean-field approxi- mation of quantum electrodynamics that allows to study relativistic electrons interacting with the vacuum. It is a variational model in which states are represented by Hilbert- Schmidt operators. We prove a charge renormalisation formula that holds close to the non-relativistic limit: the density of a ground state is shown to be integrable although such a state is known not to be trace-class. We prove that we can take the non-relativistic limit by keeping track of the vacuum polarisation. We get an altered Hartree-Fock model due to the screening effect.
Subjects / Keywordsground states; charge renormalisation; Bogoliubov-Dirc-Fock model; Dirac operator
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