Bound-state QED solutions of the photons off-shell propagating behavior in atoms

We use the S-matrix formalism of bound-state QED to study the photon-atom scattering. We find that the internal lines in Feynman diagrams which describing the propagation of off-shell bound electrons provide the off-shell amplitudes of photons' propagation in atoms phenomenally. Our work set up the connection between the property of Feynman propagators in bound-state QED and the superluminal but casual propagating behavior of light in atomic media. We also studied the relation between the bound-state QED and the widely used light-atom interacting model in quantum optics, and give the experimental condition where only the bound-state QED is valid.