New Developments in Mathematical Physics : Proceedings of the XX. Internationale Universitätswochen Für Kernphysik 1981 Der Karl-Franzens-Universität Graz at Schladming (Steiermark, Austria), February 17-26, 1981

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) © 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 Front Matter....Pages I-VII Foreword....Pages 1-1 Classical Scattering Theory....Pages 3-28 Geometric Methods in Scattering Theory....Pages 29-63 Three-Body Coulomb Scattering....Pages 65-110 Inverse Spectral and Scattering Theory....Pages 111-155 Time Delay of Quantum Scattering Processes....Pages 157-208 Finiteness of Total Cross-Sections....Pages 209-233 Analyticity Properties of the S-Matrix: Historical Survey and Recent Results in S-Matrix Theory and Axiomatic Field Theory....Pages 235-328 Scattering in Quantum Field Theory: The M.P.S.A. Approach in Complex Momentum Space....Pages 329-400 Geometrical Aspects of Gauge Configurations....Pages 401-432 A Brief Introduction to the Geometry of Gauge Fields....Pages 433-476 The Geometry of Symmetry Breaking in Gauge Theories....Pages 477-490 Geometric Aspects of Quantized Gauge Theories....Pages 491-524 Recent Developments in Finite Energy (Topological) Monopole Theory....Pages 525-575 On The Universal Low Energy Limit in Nonrelativistic Scattering Theory....Pages 577-585 On Classical Time Delay....Pages 587-598 A Finite-Energy Su(3) Solution Which Does Not Satisfy the Bogomolny Equations....Pages 599-603 $$\rm {\tilde S}O_0$$ (3.2)-Invariant Scattering of Dirac Singletons....Pages 605-611 Generating Multimonopoles by Soliton Theoretic Method....Pages 613-625 Remarks on Lattice Gauge Models....Pages 627-639 The Klein-Kaluza Theory with a Torsion....Pages 641-652 Attempts at a Geometrical Understanding of Higgs Fields....Pages 653-660 Monopoles in SU2-Yang-Mills Theory....Pages 661-663 Extended Kaluza-Klein Unified Gauge Theories....Pages 665-670 Rigorous Estimates of the Elastic e − (μ − p) Scattering Amplitude....Pages 671-678 On the Relation Between Bare and Dressed Charge in QED....Pages 679-682 Decomposition of the Coherence Relation in C*-Algebraic Many Body Physics....Pages 683-687 Optical Theorem for Three-Three Scattering....Pages 689-693 On the Determination of πN Phase Shifts from Isospin Constraints and Fixed t Analyticity....Pages 695-701