Ebook: Recent Developments in Mathematical Physics: Proceedings of the XXVI Int. Universitätswochen für Kernphysik Schladming, Austria, February 17–27, 1987

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.

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Content:
Front Matter....Pages I-XI
Circle Mappings....Pages 1-17
Dirac’s Theory of Constraints....Pages 18-52
Some Properties of Bound States in Potentials....Pages 53-79
Wiener Measure Regularization for Quantum Mechanical Path Integrals....Pages 80-99
Schr?dinger Operators with Random and Almost Periodic Potentials....Pages 100-101
The Dynamical Entropy of Quantum Systems....Pages 102-136
Hamiltonian Approach to the Theory of Anomalies....Pages 137-159
Phase Space Expansions in Quantum Field Theory....Pages 160-183
Berezin’s Pseudodifferential Forms....Pages 184-190
Classical Non-Linear ?-Models on Grassmann Manifolds....Pages 191-195
On Relativistic Irreducible Quantum Fields Fulfilling CCR....Pages 196-200
Krein’s Spectral Shift Function and Supersymmetric Quantum Mechanics....Pages 201-206
Lattice Gauge Theories with Continuous Time and Decimation....Pages 207-213
Some Aspects of the Boson-Fermion (In-) Equivalence....Pages 214-218
Optimization of Real-Space Renormalization-Group Transformations....Pages 219-223
Finding Quarkonia in QCD Vacuum....Pages 224-228
Quantization of Fermions in External Soliton Fields....Pages 229-233
Resolution of the U(1) Problem by Lattice Gauge Theory....Pages 234-239
On Some Recent Results for Conservation Laws in One Dimension....Pages 240-244
Some Recent Results on Stark Effect Hamiltonians....Pages 245-248
Conformal Properties of Integrable Models....Pages 249-255
Generating Functionals of 1PI-Green Functions in Gauge Field Theories....Pages 256-260
From Thirring’s Charge Renormalization to Gauge-Independent Renormalization of Yang-Mills Theories....Pages 261-263
Quantum Kinks and Vector Bundles....Pages 264-269
The Confinement Problem in QCD and SUSY....Pages 270-274
Fractional Quantum Hall Effect and Electron Lattice Formation....Pages 275-281
Gibbs Measure in Landau Gauge for Abelian Lattice Gauge Theories....Pages 282-286
On the Discrete Reconciliation of Relativity and Quantum Mechanics....Pages 287-290
Hamilton-Dirac Formulation of Supersymmetric Yang-Mills Theories....Pages 291-295
Scaling Behaviour of the Effective Chiral Action and Stability of the Chiral Soliton....Pages 296-299
On the Stochastic Representation of Supersymmetric Quantum Mechanics....Pages 300-304
Quantum Chaos and Geometry....Pages 305-312
On Supersymmetric Constraint Equations....Pages 313-316
Scattering from Magnetic Fields....Pages 317-321
Back Matter....Pages 323-326

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Content:
Front Matter....Pages I-XI
Circle Mappings....Pages 1-17
Dirac’s Theory of Constraints....Pages 18-52
Some Properties of Bound States in Potentials....Pages 53-79
Wiener Measure Regularization for Quantum Mechanical Path Integrals....Pages 80-99
Schr?dinger Operators with Random and Almost Periodic Potentials....Pages 100-101
The Dynamical Entropy of Quantum Systems....Pages 102-136
Hamiltonian Approach to the Theory of Anomalies....Pages 137-159
Phase Space Expansions in Quantum Field Theory....Pages 160-183
Berezin’s Pseudodifferential Forms....Pages 184-190
Classical Non-Linear ?-Models on Grassmann Manifolds....Pages 191-195
On Relativistic Irreducible Quantum Fields Fulfilling CCR....Pages 196-200
Krein’s Spectral Shift Function and Supersymmetric Quantum Mechanics....Pages 201-206
Lattice Gauge Theories with Continuous Time and Decimation....Pages 207-213
Some Aspects of the Boson-Fermion (In-) Equivalence....Pages 214-218
Optimization of Real-Space Renormalization-Group Transformations....Pages 219-223
Finding Quarkonia in QCD Vacuum....Pages 224-228
Quantization of Fermions in External Soliton Fields....Pages 229-233
Resolution of the U(1) Problem by Lattice Gauge Theory....Pages 234-239
On Some Recent Results for Conservation Laws in One Dimension....Pages 240-244
Some Recent Results on Stark Effect Hamiltonians....Pages 245-248
Conformal Properties of Integrable Models....Pages 249-255
Generating Functionals of 1PI-Green Functions in Gauge Field Theories....Pages 256-260
From Thirring’s Charge Renormalization to Gauge-Independent Renormalization of Yang-Mills Theories....Pages 261-263
Quantum Kinks and Vector Bundles....Pages 264-269
The Confinement Problem in QCD and SUSY....Pages 270-274
Fractional Quantum Hall Effect and Electron Lattice Formation....Pages 275-281
Gibbs Measure in Landau Gauge for Abelian Lattice Gauge Theories....Pages 282-286
On the Discrete Reconciliation of Relativity and Quantum Mechanics....Pages 287-290
Hamilton-Dirac Formulation of Supersymmetric Yang-Mills Theories....Pages 291-295
Scaling Behaviour of the Effective Chiral Action and Stability of the Chiral Soliton....Pages 296-299
On the Stochastic Representation of Supersymmetric Quantum Mechanics....Pages 300-304
Quantum Chaos and Geometry....Pages 305-312
On Supersymmetric Constraint Equations....Pages 313-316
Scattering from Magnetic Fields....Pages 317-321
Back Matter....Pages 323-326
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