Geodesic
Local two-particle quasipotential in the relativistic three-body problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 1, pp. 42-51 
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/
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     title = {Local two-particle quasipotential in the relativistic three-body problem},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] A. N. Kvinikhidze, D. Ts. Stoyanov, Preprint E2-5771, JINR, 1971

[2] L. D. Faddeev, ZhETF, 39 (1960), 1459 ; ДАН СССР, 138 (1961), 565 ; 145 (1962), 301 ; Тр. Матем. института им. Стеклова, 69, 1963 | MR | MR | MR | Zbl

[3] A. A. Logunov, A. N. Tavkhelidze, Nuovo Cim., 29 (1963), 380 | DOI | MR

[4] A. N. Tavkhelidze, Lectures on Quasipotential Method in Field Theory, Tata Institute of Fundamental Research, Bombay, 1964; В. Т. Кадышевский, А. Н. Тавхелидзе, Сборник, посвященный 60-летию Н. Н. Боголюбова, «Наука», 1969, 261

[5] A. N. Kvinikhidze, D. Ts. Stoyanov, Preprint E2-5746, JINR, 1971 | MR