%0 Journal Article %T A Minimization Method for Relativistic Electrons in a Mean-Field Approximation of Quantum Electrodynamics %A Christian Hainzl %A Mathieu Lewin %A Eric Sere %A Jan Philip Solovej %J Physics %D 2007 %I arXiv %R 10.1103/PhysRevA.76.052104 %X We study a mean-field relativistic model which is able to describe both the behavior of finitely many spin-1/2 particles like electrons and of the Dirac sea which is self-consistently polarized in the presence of the real particles. The model is derived from the QED Hamiltonian in Coulomb gauge neglecting the photon field. All our results are non-perturbative and mathematically rigorous. %U http://arxiv.org/abs/0706.1486v1