Stability of matter for the Hartree-Fock functional of the relativistic electron-positron field

Abstract

We investigate stability of matter of the Hartree-Fock functional of the relativistic electron-positron field -- in suitable second quantization -- interacting via a second quantized Coulomb field and a classical magnetic field. We are able to show that stability holds for a range of nuclear charges $Z_1,..,Z_K\leq Z$ and fine structure constants $\alpha$ that include the physical value of $\alpha$ and elements up to holmium ($Z=67$).