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Starting from a formal Hamiltonian as found in the physics literature --omitting photons -- we define a renormalized Hamiltonian through charge andmass renormalization. We show that the restriction to the one-electron subspaceis well-defined. Our construction is non-perturbative and does not use acut-off. The Hamiltonian is relevant for the description of the Lamb shift inmuonic atoms.Comment: Reformulation of main theorem, minor changes in the proo

Non-Perturbative Mass and Charge Renormalization in Relativistic No-Photon Quantum Electrodynamics