Annihilation superradiance in a system of positronium atoms and positron polarization of the medium

Theory of annihilation superradiation in a system of parapositronion atoms at twophoton annihilation is formulated. A new equation is derived which describes the propagation of the annihilation radiation in the positronium medium on the basis of the interaction positronium atoms via the field of virtual photons. This interaction is treated as the fourth order effect in quantum electrodynamics. Using the equations obtained for the atomic and field variables, kinetics of annihilation superradiation is studied.