Collisionless transport equation for photons in a moving medium

A collisionless transport equation is derived from Maxwell's equations for photons in a nonrandom moving medium. An effective metric tensor, which depends on the 4-velocity of the medium and the refractive index, is used in the material equations. The equations for the density matrix of the photons, written down in the relativistic Wigner representation, give the required transport equation on the transition to the approximation of geometrical optics. This equation makes it possible to determine not only the intensity of the electromagnetic radiation in the medium but also its polarization. The mean Minkowski and Abraham energy-momentum tensors are calculated and their physical meaning is discussed.