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Pré-Publication, Document De Travail Année : 2014

Charge renormalisation in a mean-field approximation of QED

Résumé

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.
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Dates et versions

hal-00909168 , version 1 (26-11-2013)
hal-00909168 , version 2 (15-05-2014)

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Citer

Jérémy Sok. Charge renormalisation in a mean-field approximation of QED. 2014. ⟨hal-00909168v2⟩
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