On the stability of the relativistic electron-positron field

We study the energy of relativistic electrons and positrons interacting through the second quantized Coulomb interaction and a self-generated magnetic field. As states we allow generalized Hartree-Fock states in the Fock space. Our main result is the assertion of positivity of the energy, if the atomic numbers and the fine structure constant are not too big. We also discuss the dependence of the result on the dressing of the electrons (choice of subspaces defining the electrons).