One-loop calculations of photon splitting in a relativistic quantum plasma by the Green function method

Homogeneous and isotopic plasma of electrons and positrons is considered. Coefficients of covariant expansion of three-photon vertex in one-loop approximation of a technique of the Green temperature functions have been calculated and as a result amplitudes of different processes probability with the participation of three photons giving the data on the polarization state probability of incoming and outgoing photons in the splitting process. Sequences of all exact symmetries, which must be accomplished for vertex tensor, have been checked from calculational results. A case of charge-symmetrical plasma and a special case of photon collinearity have been considered