  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.
