Geodesic
Three-dimensional formulation of the relativistic two-body problem in terms of rapidities
Teoretičeskaâ i matematičeskaâ fizika, Tome 30 (1977) no. 3, pp. 333-345

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A scheme is developed which is based on the three-dimensional relativistic equation of the quasipotential type [1–4]. As a main variable the authors use the rapidity, i.e. the quantity which is canonically conjugated to the relativistic relative distance [5]. A free Green function has a simple pole in the complex plane of the rapidity, which guarantees the elastic unitarity in the case of a real potential. In the case of local potential, the corresponding equation for the partial wave function in the configurational $r$-representation is the second order differential equation. The question about formulating boundary conditions is investigated, which represents a nontrivial problem in the relativistic configurational space. Exact solutions of theequation in several simple cases are found. 
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     author = {I. V. Amirkhanov and G. V. Grusha and R. M. Mir-Kassimov},
     title = {Three-dimensional formulation of the relativistic two-body problem in terms of rapidities},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {333--345},
     publisher = {mathdoc},
     volume = {30},
     number = {3},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1977_30_3_a4/}
}
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I. V. Amirkhanov; G. V. Grusha; R. M. Mir-Kassimov. Three-dimensional formulation of the relativistic two-body problem in terms of rapidities. Teoretičeskaâ i matematičeskaâ fizika, Tome 30 (1977) no. 3, pp. 333-345. http://geodesic.mathdoc.fr/item/TMF_1977_30_3_a4/