I am looking for a reference or derivation of the non-relativistic bound states of hydrogen in an electromagnetic field that include Zeeman effect, Stark shift, and Lamb shift. I am looking for a full QED treatment. I have seen Scully and Zubairy *Quantum Optics* but they only provide a rough approximation.

I am finding that those who are doing QED are mostly interested in high-energy particle physics, whereas I am interested in atomic physics and the terms relevant to corrections of the spectral line energies (resonances in QFT parlance).

I have used the Dirac equation in the low energy limit to arrive at terms for relativistic correction, spin-orbit interaction, and Darwin term, what I would like to be able to do is write out a derivation that includes the electron self-interaction term; that is a derivation with a more explicit treatment than Scully of the quantum vacuum for the Lamb shift.