3-DIMENSIONAL MANIFESTLY POINCARE-INVARIANT APPROACH TO THE RELATIVISTIC 3-BODY PROBLEM

A three-dimensional manifestly Poincare-invariant approach to the rela tivistic three-body problem is developed that satisfies the requiremen t of cluster separability and at the same time does not lead to so-cal led spurious states devoid of physical meaning. It is shown that these requirements make it possible to fix the form of the operators of the two-body interactions. The problem is solved with allowance for the d ependence of the interaction operators on the spectral parameter. This dependence is a manifestation of the structure of the particles in th e three-body system (i.e., it reflects the circumstance that the compl ete Hilbert space of state vectors of the system includes not only thr ee-body configurations of the original particles) and leads to the app earance of certain factors in the cross sections of physical processes . Two alternative formulations of the method are investigated. In the first formulation, equations are written down for the amplitudes of tr ansitions between free-particle states. In the second formulation, the states of interacting particles in the two-body scattering channels a re used as complete orthogonal bases. Partial-wave expansions of the e quations with respect to states with given total angular momentum of t he system in the helicity basis are made.