Non-Perturbative Mass and Charge Renormalization in Relativistic No-Photon Quantum Electrodynamics
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Starting from a formal Hamiltonian as found in the physics literature -- omitting photons -- we define a renormalized Hamiltonian through charge and mass renormalization. We show that the restriction to the one-electron subspace is well-defined. Our construction is non-perturbative and does not use a cut-off. The Hamiltonian is relevant for the description of the Lamb shift in muonic atoms.
Reformulation of main theorem, minor changes in the proof
Reformulation of main theorem, minor changes in the proof