  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.
