Perturbation theory for the Bethe-Salpeter equation in the plane-wave electromagnetic field

Completeness and orthogonality of the Bethe-Salpeter type equation solutions have been provide. Correct derivation of the perturbation theory formulas is presented. Generalization of this theory in the plane-wave electromagnetic field is suggested. One-quantum annihilation rate of positronium has been calculated in this field. If one-quantum decay is allowed, stationary states of the system are found for states of light positronium