Classical "Dressing" of a Free Electron in a Plane Electromagnetic Wave

The energy and momentum densities of the fields of a free electron in a plane electromagnetic wave include interference terms that are the classical version of the ``dressing'' of the electron the arises in a quantum analysis. The transverse mechanical momentum of the oscillating electron is balanced by the field momentum resulting from the interference between the driving wave and the static part of the electron's field. The interference between the wave and the oscillating part of the electron's field leads to a longitudinal field momentum and a negative field energy that compensate for the longitudinal momentum and kinetic energy of the electron. The interference terms are dominated by the near zone, so that as the wave passes the electron by the latter reverts to its energy and momentum prior to the arrival of the wave.