  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.
