New Developments in Mathematical Physics: Proceedings of the XX. Internationale Universitätswochen für Kernphysik 1981 der Karl-Franzens-Universität Graz at Schladming (Steiermark, Austria),(23/1981 Few-Body Systems)

The papers contained in this volume are lectures and seminars presented at the 20th "Universitatswochen fUr Kernphysik" in Schladming in February 1981. The goal of this school was to review some rapidly developing branches in mathematical physics. Thanks to the generous support provided by the Austrian Federal Ministry of Science and Research, the Styrian Government and other sponsors, it has been possible to keep up with the - by now already traditional - standards of this school. The lecture notes have been reexamined by the authors after the school and are now published in their final form, so that a larger number of physicists may profit from them. Because of necessary limitations in space all de- tails connected with the meeting have been omitted and only brief outlines of the seminars were incl~ded. It is a pleasure to thank all the lecturers for their efforts, which made it possible to speed up the publi- cation. Thanks are also due to Mrs. Krenn for the careful typing of the notes. H. Mitter L. Pittner Acta Physica Austriaca, Supp\. XXIII, 3-28 (1981) (c) by Springer-Verlag 1981 CLASSICAL SCATTERING THEORY+ by W. THIRRING Institut fur Theoretische Physik Universitat Wien, Austria 1. INTRODUCTION It was first recognized by Hunziker [1] that the notions of scattering theory play an important role in classical mechanics. It turned out [2] that it leads to non-trivial information for the global properties of the solutions of the classical trajectories.

Table of Contents:
Foreword.- Lectures.- Classical Scattering Theory.- Geometric Methods in Scattering Theory.- Three-Body Coulomb Scattering.- Inverse Spectral and Scattering Theory.- Time Delay of Quantum Scattering Processes.- Finiteness of Total Cross-Sections.- Analyticity Properties of the S-Matrix: Historical Survey and Recent Results in S-Matrix Theory and Axiomatic Field Theory.- Scattering in Quantum Field Theory: The M.P.S.A. Approach in Complex Momentum Space.- Geometrical Aspects of Gauge Configurations.- A Brief Introduction to the Geometry of Gauge Fields.- The Geometry of Symmetry Breakingin Gauge Theories.- Geometric Aspects of Quantized Gauge Theories.- Recent Developments in Finite Energy (Topological) Monopole Theory.- Seminars.- On the Universal Low Energy Limit in Nonrelativistic Scattering Theory.- On Classical Time Delay.- A Finite-Energy SU(3) Solution Which Does not Satisfy the Bogomolny Equations.- $$\rm {\tilde S}O_0$$ (3.2)-Invariant Scattering of Dirac Singletons.- Generating Multimonopoles by Soliton Theoretic Method.- Remarks on Lattice Gauge Models.- The Klein-Kaluza Theory with a Torsion.- Attempts at a Geometrical Understanding of Higgs Fields.- Monopoles in SU2-Yang-Milis Theory.- Extended Kaluza-Klein Unified Gauge Theories.- Rigorous Estimates of the Elastic e¯ (µ¯p) Scattering Amplitude.- On the Relation Between Bare and Dressed Charge in QED.- Decomposition of the Coherence Relation in C*-Algebraic Many Body Physics.- Optical Theorem for Three-Three Scattering.- On the Determination of tN Phase Shifts from Isospin Constraints and Fixed t Analyticity.