On energy and momentum conservation laws for an electromagnetic field in a medium or at diffraction on a conducting plate

For a field-matter system, general nonstationary balance equations for energy and momentum densities and their transport velocities are obtained based on a rigorous nonstationary definition of these densities depending on the creation history of the field. We analyze the simplest dispersion law determined by conductivity dissipation; we find the electromagnetic energy density, phase velocity, group velocity, and energy and momentum transport velocities of a plane monochromatic wave. The low-frequency energy density is shown to be given by the electrostatic density in which the dielectric constant is replaced with its real part and the energy transport velocity is equal to the phase velocity. The group velocity can exceed the speed of light. We prove that the Minkowski form of momentum density must be used in the medium, and find the corresponding transport velocity, which in the case under consideration also coincides with the phase velocity. Energy and momentum conservation laws are shown to hold for a plane electromagnetic wave propagating in a medium or diffracted by a conducting plate.