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Full Description
This volume contains the written versions of invited lectures and abstracts of seminars presented at the 26th "Universitatswochen fiir Kernphysik" (Uni versity nuclear physics weeks) in Schladming, Austria, in February 1987. Again the generous support of our sponsors, the Austrian Ministry of Sci ence and Research, the Styrian government and others, made it possible to invite expert lecturers. The meeting was organized in honour of Prof. Dr. th Walter Thirring in connection with his 60 birthday. In choosing the topics for the lectures we have tried to cover a good many of the areas in which mathematical physics has made significant progress in recent years. Both classical and quantum mechanical problems are considered as well as prob lems in statistical physics and quantum field theory. The common feature lies in the methods of mathematical physics that are used to understand the underlying structure and to proceed towards a rigorous solution. Thanks to the efforts of the speakers this spirit was maintained in all lectures. Due to space limitations only shortened versions of the many seminars presented in Schladming could be included. After the school the lecture notes were revised by the authors, whom we thank for their efforts, which made it possible to speed up publication. Thanks are also due to Mrs. Neuhold for the careful typing of the notes, and to Miss Koubek and Mr. Preitler for their help in proofreading.
Contents
Circle Mappings.- Dirac's Theory of Constraints.- Some Properties of Bound States in Potentials.- Wiener Measure Regularization for Quantum Mechanical Path Integrals.- Schrödinger Operators with Random and Almost Periodic Potentials.- The Dynamical Entropy of Quantum Systems.- Hamiltonian Approach to the Theory of Anomalies.- Phase Space Expansions in Quantum Field Theory.- Berezin's Pseudodifferential Forms.- Classical Non-Linear ?-Models on Grassmann Manifolds.- On Relativistic Irreducible Quantum Fields Fulfilling CCR.- Krein's Spectral Shift Function and Supersymmetric Quantum Mechanics.- Lattice Gauge Theories with Continuous Time and Decimation.- Some Aspects of the Boson-Fermion (In-) Equivalence.- Optimization of Real-Space Renormalization-Group Transformations.- Finding Quarkonia in QCD Vacuum.- Quantization of Fermions in External Soliton Fields.- Resolution of the U(1) Problem Lattice Gauge Theory.- On some Recent Results for Conservation Laws in One Dimension.- Some Recent Results on Stark Effect Hamiltonians.- Conformal Properties of Integrable Models.- Generating Functionals of 1PI-Green Functions in Gauge Field Theories.- From Thirring's Charge Renormalization to Gauge-Independent Renormalization of Yang-Mills Theories.- Quantum Kinks and Vector Bundles.- The Confinement Problem in QCD and SUSY.- Fractional Quantum Hall Effect and Electron Lattice Formation.- Gibbs Measure in Landau Gauge for Abelian Lattice Gauge Theories.- On the Discrete Reconciliation of Relativity and Quantum Mechanics.- Hamilton-Dirac Formulation of Supersymmetric Yang-Mills Theories.- Scaling Behaviour of the Effective Chiral Action and Stability of the Chiral Soliton.- On the Stochastic Representation of Supersymrnetric Quantum Mechanics.- Quantum Chaos and, Geometry.-On Supersymrnetric Constraint Equations.- Scattering from Magnetic Fields.- Index of Contributors.
