Holographies and EXAFS in quantum electrodynamics

We calculate the cross section of the photoionization process consistently in the framework of quantum electrodynamics, including the initial-state photon interaction and the final-state photoelectron interaction with neighboring atoms. The obtained photoionization cross section explains multiple energy x-ray holography (MEXH), photoelectron holography, and extended x-ray absorption fine structure (EXAFS). In EXAFS, the contribution of the initial-state photon interaction is found to oscillate with energy and can disturb the EXAFS signal. It becomes non-negligible at higher energies. At 1 keV above the absorption edge, it can be in comparable order of the EXAFS signal. The hologram functions of MEXH and x-ray fluorescence holography are consistent with those in classical electrodynamics.