Quantum Electrodynamics in a Photon Sea

Thermal photons are present in every initial state, and nonthermal photons are present in many systems of interest. Furthermore, stimulated emission promotes the infrared divergence of quantum electrodynamics from logarithmic to an inverse power in a Planck distribution. I have calculated to order $e^2$ the background-photon corrections to the cross section for scattering a charged particle off an external Coulomb potential. I demonstrate the cancelation of infrared divergences, and derive a formal shift in the masses of charged particles. I interpret this shift, and discuss atomic spectra.