Abstract:
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 rr-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.
Citation:
I. V. Amirkhanov, G. V. Grusha, R. M. Mir-Kassimov, “Three-dimensional formulation of the relativistic two-body problem in terms of rapidities”, TMF, 30:3 (1977), 333–345; Theoret. and Math. Phys., 30:3 (1977), 212–221
\Bibitem{AmiGruMir77}
\by I.~V.~Amirkhanov, G.~V.~Grusha, R.~M.~Mir-Kassimov
\paper Three-dimensional formulation of the relativistic two-body problem in terms of rapidities
\jour TMF
\yr 1977
\vol 30
\issue 3
\pages 333--345
\mathnet{http://mi.mathnet.ru/tmf2800}
\transl
\jour Theoret. and Math. Phys.
\yr 1977
\vol 30
\issue 3
\pages 212--221
\crossref{https://doi.org/10.1007/BF01036713}
Linking options:
https://www.mathnet.ru/eng/tmf2800
https://www.mathnet.ru/eng/tmf/v30/i3/p333
This publication is cited in the following 2 articles:
I. V. Amirkhanov, G. V. Grusha, R. M. Mir-Kassimov, “Analytic properties of quasipotential scattering amplitude in the complex planes of the rapidity and the angular momentum”, Theoret. and Math. Phys., 40:3 (1979), 814–821
M. Kh. Khankhasaev, “Equation for the total scattering amplitude in the variable phase approach”, Theoret. and Math. Phys., 34:2 (1978), 106–112
Citation in format AMSBIB
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