A finite quantum electrodynamical base for many photon collective phenomena

Abstract

We analyze the interaction of many ’’nonoverlapping’’ atoms with the common radiation field of transverse photons over a continuum of modes. Typical effects of quantum optics arising from this interaction require extensions to very high powers in the coupling constant e and diverge therefore within a systematic perturbation approach. Since renormalization to such high orders is not feasible in practice, we formulate for the purpose of quantum optics ’’a new peace treaty between QED and its infinities.’’ This is a compromise between the necessity of including effects of very high powers in e and the trivial demands for finite results. We show that a unitary time evolution operator exists if, in essence, only any finite number of levels of each atom is treated as ’’existent.’’ We convince ourselves that the limits of the concept of ’’nonoverlapping atoms’’ are reached long before any infinities can enter. The resulting theories meet still reasonable requirements with respect to the dualism of light, Dicke principle, and causality. They are formulated so that some practical demands of quantum optics (homogeneous and inhomogeneous line broadening, Doppler effects) can be met easily if desired.