Photon splitting cascades and a new statistics

Photon splitting cascades in a magnetic field are considered. It is shown, in the stochastic limit approximation, that photons in cascades might form entangled states (``triphons'') and that they obey not Bose but a new type of statistics, the so called infinite or quantum Boltzmann statistics. These states belong to an interacting Fock space which is a generalization of the ordinary Fock space. The new photon statistics in principle can be detected in future astrophysical experiments such as the planned Integral mission and also in nonlinear quantum optics.