Abstract
The minimal-coupling Hamiltonian for a nonrelativistic hydrogenic atom interacting with a photon field in the \ensuremath{\alpha}-Lorentz gauge is canonically gauge transformed to one with four arbitrary degrees of gauge freedom. The theory, nonrelativistic in the charge dynamics, is wholly covariant in its treatment of the scalar, transverse, and longitudinal electromagnetic fields. One degree of gauge freedom of the transformed Hamiltonian comes from the arbitrary scalar parameter contained within the \ensuremath{\alpha}-Lorentz gauge, while the others come from arbitrary parameters governing the gauge transformation. A Jaynes-Cummings-type model is constructed by suitable restrictions to the gauge freedom, and found to display an admixture of transverse and scalar interactions but no longitudinal component. The model gives the Lamb shift, correct to the second order of the electronic charge consistent with relativistic quantum electrodynamics.
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