Geodesic
Relativistic three-body problem in relative variables
Teoretičeskaâ i matematičeskaâ fizika, Tome 10 (1972) no. 3, pp. 338-348

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A Lorentz covariant three-body theory is constructed in the momentum representation in the framework of the three-dimensional formulation of quantum field theory. Relativistic Jacobian momenta are introduced by means of the operation of composition of four-vectors in Lobachevskii space. It is shown that the cms motion can be separated out and the problem is formulated solely in relative variables as a direct generalization of the nonrelativistic theory. Three-dimensional relativistic analogs are obtained of the Faddeev equations for the scattering amplitude and also an analog of the Schrödinger equation in relative variables for a three-body system. The formulation satisfies three-particle unitarity and the correspondence principle. 
@article{TMF_1972_10_3_a2,
     author = {V. M. Vinogradov},
     title = {Relativistic three-body problem in relative variables},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {338--348},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1972_10_3_a2/}
}
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V. M. Vinogradov. Relativistic three-body problem in relative variables. Teoretičeskaâ i matematičeskaâ fizika, Tome 10 (1972) no. 3, pp. 338-348. http://geodesic.mathdoc.fr/item/TMF_1972_10_3_a2/