  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.
