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

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

1999-10-06

arxiv.org/abs/math/9910033v1

Mathematics

Analysis of PDEs

68 pages; AMS Latex

Scientific paper

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.

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