The piNNN--NNN problem. Connectedness, transition amplitudes and quasi-particle approximation
In this paper we review the present status of the piNNN--NNN problem. In particular, we re-consider the chain-labelled approach recently proposed by us, and identify a class of graphs, previously overlooked, which prevents the kernel of the corresponding piNNN--NNN equations from being connected. We propose some pproximate schemes, yielding connected-kernel equations. A generalization of the residue method allows to relate the transition amplitudes for the coupled piNNN--NNN system to the chain-labelled formalism. The quasi-particle approach is extended to the present situation, where emission/absorption of particles is allowed. The open problems for the piNNN--NNN system in the light of the present and of previous approaches are finally discussed.