Dispersion Relations for Fixed-Source Meson Theories

Dispersion relations for a class of Hamiltonian operators describing meson theories with a fixed, extended source are derived for meson-nucleon scattering. It is assumed that each meson field operator is coupled to its own source, and a restriction is imposed on the maximum number of temporal or spatial derivatives of the field operator that can occur in any one term. On the other hand, the interaction need not be linear in the meson field. With these assumptions, nonrelativistic versions of all proposed relativistic dispersion relations are derived rigorously. In particular, the $P$-wave equations of Chew and Low are obtained, as well as a set of equations for the $S$ waves.