Primary Singularities, Asymptotic Wave Functions and Unitarity in the Three-Body Problem

This paper studies the singular pole structure present in the momentum space three-body-scattering wave functions. We prove that this structure alone is entirely responsible for the asymptotic behavior in coordinate space. We are also able to prove, without further assumptions, that the residues of each of the singularities in the wave function must be physical scattering amplitudes. We extend our study of these primary poles in three-body physics by using the singularity structure to obtain a derivation of the on-shell unitarity relations.