Macroscopic averages in QED in material media

This article addresses the problem of whether it is possible to describe the effect of the atoms of material media on the field only in terms of a dielectric constant, in the regime where the field has to be treated quantum mechanically. Using a simple model of a linear lossless material medium, we start from first principles and determine the validity of the approximations required to obtain such a quantum analogue of classical macroscopic electrodynamics. This theory is derived here from the fundamental microscopic QED description of a medium, in terms of its constituent atoms in the vacuum, by taking macroscopic averages of the dynamical variables. The condition of the validity of the macroscopic approximation is obtained as the proviso for neglecting the contribution of the atoms of the medium to the quantum noise of the field. We show that macroscopic averaging is compatible with a quantum theory and does not imply any smoothening of the intrinsic quantum fluctuations of the field. Although this theory is based on a simple one-dimensional model of a single-mode cavity, it is able to describe the frequency dependence of the dielectric constant.5553832384