Extension of the Sp(2,C) group for description of a three-body system - Yaroshenko, A.P.; Uvarov, I.V. (Вопросы атомной науки и техники, 2012)
We propose a new approach to the three-body problem that is based on the extension of the Sp(2,C) group, which is the universal covering group for the Lorentz group, to the Sp(4,C) one. Angular momenta of the particles in the phase space of a system with an inner interaction are obtained. This result can be used to obtain eigenfunctions of angular momenta, and exact quantum mechanical solutions for the system defined by Dirac-like equations, e.g. a system of three zero-spin particles or Regge trajectories of N-baryons.