Many-Body Problem in Quantum Field Theory, III

The general procedures described in I and II to deal with the scattering problems involving composite particles are illustrated in this paper for the interacting scalar meson and scalar photon fields.Utilizing Wick’s solution for the covariant two-body equation (Bethe-Salpeter equation), the following problems are discussed:(1) the normalization of the Feynman amplitude for the bound state corresponding to Wick’s solution,(2) the disintegration of the bound state by a scalar photon,(3) the Rutherford scattering of the composite particle.In appendices some general remarks are given on the reciprocal nature of the present formalism and on the asymptotic forms of the Feynman emplitudes.