Local two-particle quasipotential in the relativistic three-body problem

A study is made of the possibility of using in the three-dimensional relativistic equations for a three-body system a quasipotential that in the approximation of a binary interaction contains “local” two-particle quasipotentials. It is shown that the part of such a quasipotential that corresponds to binary interactions can be expressed in a definite manner in terms of the physical two-particle scattering amplitudes irrespective of an expansio of these amplitudes in a small coupling constant. It is shown that all 16 scattering amplitudes, obtained as solutions of these three-particle equations, are equal to the physical amplitudes on the mass shell.