Propagation of singularities in many-body scattering

In this paper we describe the propagation of singularities of tempered dist ributional solutions u is an element of S ' of (H - lambda )u = o, lambda > 0, where H is a many-body Hamiltonian H = Delta + V, Delta greater than or equal to 0, V = Sigma V-a(a), under the assumption that no subsystem has a bound state and that the two-body interactions V-a are real-valued polyhom ogeneous symbols of order -1 (e.g. Coulomb-type with the singularity at the origin removed). Here the term 'singularity' provides a microlocal descrip tion 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 assumpt ions, is all of the S-matrix) is given by the broken geodesic flow, broken at the 'singular directions', on Bn-l at time rr. We also present a natural geometric generalization to asymptotically Euclidean spaces. (C) 2001 Edit ions scientifiques et medicales Elsevier, SAS.