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              <p>In this note, we consider an Hamiltonian, with ultraviolet and infrared cutoffs, describing the interaction of relativistic electrons and positrons in a Coulomb potetial 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 constatnt</p>
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