The quantum electrodynamics of relativistic bound states with cutoffs. I

In this note, we consider a Hamiltonian with ultraviolet and infrared cutoffs describing the interaction of relativistic electrons and positrons in a Coulomb potential with transversal photons in Coulomb gauge. We prove that the Hamiltonian is self-adjoint in the Fock space and has a ground state for a sufficiently small coupling constant.

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