Multiple Poles in the Scattering Green's Function

A general theory of multiple poles in the scattering Green's function is developed. It is shown that their residues are determined by certain generalized Bethe-Salpeter equations apart from an over-all multiplicative factor. As an example of multiple poles, the zero-energy case is considered in the Wick-Cutkosky model. By means of an integral representation, the generalized Bethe-Salpeter equations are converted into simultaneous one-dimensional integral equations. Exact solutions are obtained to these equations of the first order. The results are compared with Heisenberg's dipole-ghost theory and with the quantum electrodynamics of Gupta and Bleuler.