PHENOMENOLOGICAL QUANTUM ELECTRODYNAMICS IN PERIODIC DIELECTRIC MEDIA

The quantization of the x-ray field in a crystalline medium phenomenologically described by a periodic dielectric susceptibility chi(r) is carried out exactly, that is, the usual approximation of the dynamical theory of x-ray diffraction of neglecting terms that are of second and higher orders in chi is not employed. This can be achieved after exact orthogonality relations for the classical electromagnetic Bloch waves are obtained. This formalism provides a simple framework for the study of a number of QED processes involving x-ray photons undergoing diffraction in a crystal. As a brief application, we show that the interaction of the quantized radiation field with an arbitrary classical current, i.e., the radiation of coherent states of Bloch photons can be studied along lines similar to the analogous situation in vacuum. The emission of such x-ray Bloch photons is governed by Poisson distributions.