Hydrogen in an electromagnetic field bound states for full quantum electrodynamics 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.
 A: Let us state first the idea behind QED. QED stands for quantum electrodynamics and it has two main components that are merged. One the one hand special relativity (SR) on the other quantum mechanics. The first one concerns very high speeds or high energies, the second one pertains very small things. If you have a Hydrogen atom just sitting there there is no need to include (SR) effects. Same as, if your system is to big, there is no need to use quantum mechanics.
With that cleared out, you should understand the different origins of the effects you are speaking of. The Lamb shift has to do with the vacuum polarization (or electron self-energy), or if you want the "dressing" of the photon propagator. As can be seen in most books of quantum field theory (QFT), it is related to the Uehling term correction to the Coulomb potential. We could call this an intrinsic effect.
The Zeeman and Stark effects are different in origin. They appear through external fields. This means they will not pop out of QED without modifying anything else. You should be asking then how to model external fields within QED and you will have to look for effective field theories (EFTs).
In the context of EFTs, one essentially finds an effective field theory by some method/approximation. There are several ways to speak about effective theories, but I believe you might be interested in expanding your theory around external backgrounds.
I hope there are enough keywords to point you in some useful direction.
A: Sections 2-8 and 4-7 of Sakurai, J. J. (1967) Advanced Quantum Mechanics give derivations of the Lamb Shift and electron self-interaction from the perspective of quantum mechanics (Section 2) and quantum field theory (Section 4).
