Generalization and applications of the Sasakawa theory

The Sasakawa theory of scattering is phrased in the form of a Fredhohn reduction technique for integral equations possessing a fixed-point singularity in their kernels. This permits the generalization of this theory to a large variety of scattering integral equations. Some specific applications include the two-particle off-shell and multichannel scattering problems. In the first instance a rank-three approximation to the fully off-shell transition matrix is derived which is exact on and half-off shell, satisfies off-shell unitarity, and which possesses no unphysical singularities. In the second problem it is shown how the method leads to the generation of a unitary approximation to the multichannel amplitudes.