Canonical and kinetic forms of the electromagnetic momentum in an ad hoc quantization scheme for a dispersive dielectric

Abstract

An ad hoc quantization scheme for the electromagnetic field in a weakly dispersive, transparent dielectric leads to the definition of canonical and kinetic forms for the momentum of the electromagnetic field in a dispersive medium. The canonical momentum is uniquely defined as the operator that generates spatial translations in a uniform medium, but the quantization scheme suggests two possible choices for the kinetic momentum operator, corresponding to the Abraham or the Minkowski momentum in classical electrodynamics. Another implication of this procedure is that a wave packet containing a single dressed photon travels at the group velocity through the medium. The physical significance of the canonical momentum has already been established by considerations of energy and momentum conservation in the atomic recoil due to spontaneous emission, the Cerenkov effect, the Doppler effect, and phase matching in nonlinear optical processes. In addition, the data of the Jones and Leslie radiation pressure experiment is consistent with the assignment of one ?k unit of canonical momentum to each dressed photon. By contrast, experiments in which the dielectric is rigidly accelerated by unbalanced electromagnetic forces require the use of the Abraham momentum.