Propagation of singularities in many-body scattering in the presence of bound states

Abstract

We describe the propagation of singularities of tempered distributional generalized eigenfunctions of many-body Hamiltonians at non-threshold energies under the assumption that the inter-particle interactions are real-valued polyhomogeneous symbols of order -1 (e.g. Coulomb-type, but without the singularity at the origin). Here the term `singularity' refers to a microlocal description of the lack of decay at infinity. We use this result to describe the wave front relation of the S-matrices. We also analyze Lagrangian properties of this relation, which shows that the relation is not `too large' in terms of its dimension.