Covariant decomposition and polarizational selection rules for interaction among photons in a moving medium

Starting from the first principles we establish the symmetries under inversions and obtain relativistic tensorial decompositions for multiphoton amplitudes in moving isotopic homogeneous media. Basing on these decompositions we find universal selection rules with respect to polarizations for the processes of photon splitting and junction in a medium, as well as for photon-photon scattering in the vacuum. Some consequences of the selection rules obtained are considered in application to nonlinear wave processes. (author)