Jean-Marie Barbaroux, Mouez Dimassi, Jean-Claude Guillot
Quantum electrodynamics of relativistic bound states with cutoffs
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ABSTRACT.  We consider an Hamiltonian with ultraviolet and infrared cutoffs, describing the interaction of relativistic electrons and positrons in a Coulomb potential with photons in Coulomb gauge. The interaction includes both interaction of the current-density with transversal photons and the Wick ordering corrected Coulomb interaction of charge-density with itself. 
We prove that the Hamiltonian is self-adjoint and has a ground state for sufficiently small coupling constants.