The transitions $\gamma \gamma \to \nu \bar{\nu}$ and $\gamma \to \gamma \gamma$ in a strong magnetic field

The photon-neutrino process gamma gamma -> nu bar nu and photon splitting are considered in a strong magnetic field. The partial polarization amplitudes are calculated within the standard model in the limit of a strong field. The amplitudes do not depend on the field strength in this limit. Using the vector parts of the amplitudes, the process of the photon splitting gamma -> gamma gamma is investigated both below and above the pair creation threshold. The splitting probabilities are calculated taking account of the photon dispersion and large radiative corrections near the resonance