A RkLATIVISTIC “ POTENTIAL MODEL ” FOR N - PARTICLE SYSTEMS

Neither quantum field theory nor S-Matrix theory have a well defined procedure for going over to an approximation that can be reliably used in non-relativistic models for nuclear physics. We meet the problem here by constructing a finite particle number relativistic scattering theory for (scalar) particles and mesons using integral equations of the Faddeev-Yakubovsky type. Restricted to N particles and one meson, we can go from the relativistic theory to a " potential theory " in the integral equation formulation by using boundary states which do not contain the meson asymptotically. The meson-particle input amplitudes contain a pole at the particle mass, and the particle-particle input amplitudes are null. This gives unique definition (numerically calculable) to the particle-particle off-shell amplitude, and hence to the covariant " scattering potential " (but not to the non-invariant concept of " potential energy "). As we have commented before, if we take these scattering amplitudes as input for relativistic Faddeev equations, the results are identical to those obtained from the same model starting from three particles and one meson. In this paper we explore how far we can extend this relativistic " potential model " to higher numbers of particles and mesons.