Propagation of singularities in many-body scattering

Details Propagation of singularities in many-body scattering Propagation of singularities in many-body scattering

1999-06-24

arxiv.org/abs/math/9906161v1

Mathematics

Analysis of PDEs

80 pages, 3 figures; submitted for publication

Scientific paper

In this paper we describe the propagation of singularities of tempered distributional generalized eigenfunctions of many-body Hamiltonians under the assumption that no subsystem has a bound state and that the two-body interactions are real-valued polyhomogeneous symbols of order -1 (e.g. Coulomb-type with the singularity at the origin removed). Here the term 'singularity' provides a microlocal description of the lack of decay at infinity. We use this result to prove that the wave front relation of the free-to-free S-matrix (which, under our assumptions, is all of the S-matrix) is given by the broken geodesic relation, broken at the 'singular directions' (given by the collision planes) on the sphere, at time pi. We also present a natural geometric generalization to asymptotically Euclidean spaces.

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