Some results on many-body scattering theory

Abstract

Several problems are considered related to the study of the T-matrix in the manybody scattering situation. Expanding previous results, the T-matrix is studied outside the realm of perturbation theory, with relation to establishing its analytic properties under the rotation of the final momenta from real to complex values, k --> (1 + [theta])k. The geometry of the contour distortion is expressed so as to involve nonperturbative T-matrix element subblocks with incoming and outgoing momenta uniformly rotated. An unrelated elementary Hilbert space argument is given to bound the contributions of high-energy intermediate states to the resolvent identity.