These proceedings contain lectures given at the N.A.T.O. Advanced Study Institute entitled "Scattering Theory in Mathematics and Physics" held in Denver, Colorado, June 11-29, 1973. We have assembled the main series of lectures and some presented by other participants that seemed naturally to complement them. Unfortunately the size of this volume does not allow for a full account of all the contributions made at the Conference; however, all present were pleased by the number and breadth of those topics covered in the informal afternoon sessions. The purpose of the meeting, as reflected in its title, was to examine the single topic of scattering theory in as many of its manifestations as possible, i.e. as a hub of concepts and techniques from both mathematics and physics. The format of all the topics presented here is mathematical. The physical content embraces classical and quantum mechanical scattering, N-body systems and quantum field theoretical models. Left out are such subjects as the so-called analytic S-matrix theory and phenomeno logical models for high energy scattering. We would like to thank the main lecturers for their excellent presentations and written summaries. They provided a focus for the exceptionally strong interaction among the participants and we hope that some of the coherence achieved is reflected in these published notes. We have made no attempt to unify notation.
Table of ContentsScattering Theory for Dissipative Hyperbolic Systems.- Scattering Theory in Waveguides.- Nonlinear Scattering Theory.- Scattering in Classical Mechanics.- Some Questions in Non-Relativistic Quantum Scattering Theory.- Commutators and Local Decay.- Candidates for ?ac and Hac.- Regular Perturbations.- A Refinement of the Kato-Rosenblum Lemma and its Applications in Scattering Theory: Relativistic Potential Scattering, High Energy Behaviour of Scattering Cross Sections and the Time-Delay Operator.- The Gel’ Fand-Levitan Method in the Inverse Scattering Problem.- Perturbations of the Laplacian by Coulomb-Like Potentials.- Analytic Perturbation Approach to N-Particle Quantum Systems.- Spin-Wave Scattering.- An Introduction to Some Mathematical Aspects of Scattering Theory in Models of Quantum Fields.- History and Perspectives in Scattering Theory. A Strictly Personal View..