Renormalization of Dirac's Polarized Vacuum

We review recent results on a mean-field model for relativistic electrons in atoms and molecules, which allows to describe at the same time the self-consistent behavior of the polarized Dirac sea. We quickly derive this model from Quantum Electrodynamics and state the existence of solutions, imposing an ultraviolet cut-off $\Lambda$. We then discuss the limit $\Lambda\to\infty$ in detail, by resorting to charge renormalization.