Energy-Momentum Tensors for Dispersive Electromagnetic Waves

Classical relativistic field theory is used as a basis for a general discussion of the problem of splitting up the total energy-momentum tensor ofa system into contributions from its component subsystems. Both the Minkowski and Abraham forms (including electrostriction) arise naturally in alternative split-up procedures applied to a nondispersive dielectric fluid. The case of an electromagnetic wave in a (spatially and temporally) dispersive medium in arbitrary but slowly varying motion is then treated. In the dispersive case the results cannot be found by replacing the dielectric constant e with e(&, ar) but include derivatives with respect to the wave vector k and the frequency ar. Ponderomotive force expressions are obtained and the perturbation in the total energy-momentum tensor due to a one-dimensional wavepacket is found, A nonlinear Schrtidinger equation is obtained for the evolution of a three-dimensional wavepacket. Both hot and cold plasmas are treated.