Three-dimensional manifestly Poincaré-invariant approach to relativistic three-body problem

The three-dimensional manifestly Poincaré-invariant approach to the relativistic three-body problem which satisfies the requirement of the cluster separability and does not lead to unphysical so-called “spurious bound states” is developed. It is shown that these requirements determine the possible forms of the pair interaction operators. The problem is solved with allowance for the dependence of the interaction operators on the spectral parameter. This dependence caused by the structure of particles (i.  e. reflection of the fact that the total Hilbert space of the state vectors includes not only the three-body configurations) and it leads to appearance of some factors in the cross sections of the physical processes. Two alternative formulations of the method are investigated. In the first formulation the equations are written for transition amplitudes between state vectors of the free particles. In the second one the complete orthogonal sets of the state vectors of interacting particles in the two-body scattering channels are used. In the framework of the helicity formalism the partial-wave decomposition of the three-body equations for particles with arbitrary spins is performed.