Geodesic
Local two-particle quasipotential in the relativistic three-body problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 1, pp. 42-51

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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. 
@article{TMF_1973_16_1_a3,
     author = {A. N. Kvinikhidze and D. Ts. Stoyanov},
     title = {Local two-particle quasipotential in the relativistic three-body problem},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {42--51},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1973_16_1_a3/}
}
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A. N. Kvinikhidze; D. Ts. Stoyanov. Local two-particle quasipotential in the relativistic three-body problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 1, pp. 42-51. http://geodesic.mathdoc.fr/item/TMF_1973_16_1_a3/