2013/11/26 by Jérémy Sok, Sok, Jérémy
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1311.6575
arxiv created 2014/05/15 · arxiv updated 2014/05/16
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.