Astrophysically relevant processes in Lorentz-violating QED

We consider quantum electrodynamics with violation of Lorentz in-variance. We calculate the rates of photon decay along with the cross sections of electron-positron pair production on background radiation and in the Coulomb field. The latter process is essential for detection of photon-induced air showers in the atmosphere. The results of this work are written in [1] in details.