Photon splitting above the pair creation threshold in a strong magnetic field

The process of photon splitting $\gamma \to \gamma \gamma$ in a strong magnetic field is investigated both below and above the pair creation threshold. Contrary to the statement by Baier et al., the allowed'' channel $\alw$ is shown not to be a comprehensive description of splitting in the strong field because the forbidden’’ channel $\text{frb}$ is also essential. The partial amplitudes and the splitting probabilities are calculated taking account of the photon dispersion and large radiative corrections near the resonance.