Geometry and Analysis in Many-Body Scattering

This chapter explains in relatively nontechnical terms recent results in many-body scattering and related topics. Many results in the many-body setting should be understood as new results on the propagation of singularities, here understood as lack of decay of wave functions at infinity, with much in common with real principal type propagation (wave phenomena). Classical mechanics plays the role that geometric optics has in the study of the wave equation, but even at this point quantum phenomena emerge. Propagation of singularities has immediate applications to the structure of scattering matrices and to inverse scattering; these topics are addressed here. The final section studies a problem very closely related to many-body scattering, namely scattering on higher rank noncompact symmetric spaces.