  The variational approach, used by Feynman in the study of the polaron
problem, is generalized to treat a system of N 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 effective N-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 of N.
