Bounds on the coupling parameters in field theoretical models of nuclear physics

We investigate a simple meson-nucleon field theory in relativistic random phase approximation. To avoid perturbative expansions, the relativistic random phase approximation is cast into an exactly soluble model invented by Zachariasen. To make the model well defined, it is necessary to cut off nucleon-antinucleon states with invariant mass >Λ. This is achieved by introducing form factors in a consistent way. Still the elimination of unphysical ghost states implies a bound on the square of the coupling constant, which is discussed as a function of the cut off. We find that the coupling used to fit low energy properties requires a strong suppression of N-anti N-states. These results do not depend on the renormalization scheme. (orig.)