Time-dependent scattering theory of N-body quantum systems

We give a full and serf contained account of the basic results in N-body sc attering theory which emerged over the last ten years: The existence and co mpleteness of scattering states for potentials decreasing like r(-mu), mu > root3 - 1. Our approach is a synthesis of earlier work and of new ideas. G lobal conditions on the potentials are imposed only to define the dynamics. Asymptotic completeness is derived from the fact that the mean square diam eter of the system diverges like t(2) as t --> +/- for any orbit t which is separated in energy from thresholds and eigenvalues (a generalized version of Mourre's theorem involving only the tails of the potentials at large di stances). We introduce new propagation observables which considerably simpl ify the phase-space analysis. As a topic of general interest we describe a method of commutator expansions.