Quasipotential in the fourth order of perturbation theory and infrared singularities

The effects of binding on the calculation of the corrections to the hyperfine splitting of the ground level of muonium and positronium are investigated. Particular attention is devoted to the problem of the canceling of the anomalously large contributions due to the behavior of the quasipotential in the infrared region. The advantages of the first form of the quasipotential approach, using the two-time Green's function, are analyzed. The quasipotential for the interaction of two particles of equal masses in the fourth order of perturbation theory is presented.