On the Energy and Momentum Conservation Laws for Linearized Electromagnetic Fields in a Dispersive Medium

Abstract

On the basis of the “small-signal power theorem”, a “small-signal momentum theorem” is derived for the linearized electromagnetic fields in electron streams in the presence of a static magnetic field. Expressions for the field momentum, the stress tensor and the momentum dissipation of the linearized electromagnetic fields are obtained. It is proved for a quasi-monochromatic wave that the small-signal momentum (or power) theorem can be reduced to the momentum (or energy) conservation law formulated phenomenologically in terms of a reduced permittivity tensor. From this, it is found that the quasi-particles introduced from the phenomenological expression for the field energy have the momentum (or energy) density given by the “small-signal momentum (or power) theorem”.