Nonperturbative treatment of theN-body system with dynamical mesons

The variational approach, used by Feynman in the study of the polaron problem, is generalized to treat a system ofN non-relativistic particles interacting with scalar and vector mesons. After integrating out the meson fields in the path integral formulation we perform a variational calculation for the effectiveN-body two-time action to obtain the energy and the mass of the system. The interplay of self energies and exchange terms in attaining binding and saturation is examined. We estimate the size of the particles in the medium and give the mean number of mesons as a function ofN.Communicated by F. Lenz