Quantization and Infinite-Dimensional Systems

As all participants know by now, the Bialowieza Summer Workshop has acquired a life of its own. The charming venue of the meetings, the informal atmosphere, the enthusiasm of the participants and the intensity of the scientific interaction have all conspired to make these meetings wonderful learning experiences. The XIIth Workshop (held from July 1 - 7, 1993) was once again a topical meeting within the general area of Differential Geometric Methods in Physics, focusing specifically on Quantization and Infinite-dimensional Systems. Altogether, about fifty participants attended the workshop. As before, the aim of the workshop was to have a small number of in-depth lectures on the main theme and a somewhat larger number of short presentations on related areas, while leaving enough free time for private discussions and exchange of ideas. Topics treated in the workshop included field theory, geometric quantization and symplectic geometry, coherent states methods, holomorphic representation theory, Poisson structures, non-commutative geometry, supersymmetry and quantum groups. The editors have the pleasant task of first thanking all the local organizers, in particular Dr. K. Gilewicz, for their painstaking efforts in ensuring the smooth running of the meeting and for organizing a delightful array of social events. Secondly, they would like to record their indebtedness to all the people who have contributed to this volume and to the redoubtable Ms. Cindy Parkinson without whose patient typesetting and editing skills the volume could hardly have seen the light of the day. Front Matter....Pages i-ix Front Matter....Pages 1-1 Two Approaches to Toeplitz Operators on Fock Space....Pages 3-7 Quantization by Membranes and Integral Representations of Wave Functions....Pages 9-19 Noncommutative Geometry and Second Quantization....Pages 21-28 Loop Variables in Quantum Gravity and Vassiliev Invariants....Pages 29-41 Geometric Quantization of String Theory Using Twistor Approach....Pages 43-51 Infinite-Dimensional Supermanifolds of Solutions in Lagrangian Field Theories with Fermion Fields....Pages 53-60 Plücker Embedding of the Hilbert Space Grassmannian and Boson-Fermion Correspondence via Coherent States....Pages 61-66 Front Matter....Pages 67-67 Supercoherent States and Geometric Quantization of a Super Kähler Supermanifold....Pages 69-78 Holomorphic Representations and Coherent States....Pages 79-85 On the Spectrum of the Geodesic Flow on Spheres....Pages 87-92 Symplectic Realizations of the Galilei-Carroll Group....Pages 93-97 Covariant and Contravariant Berezin Symbols of Bounded Operators....Pages 99-108 On Reproducing Kernels for Holomorphic Vector Bundles....Pages 109-112 Poisson Structures, Stability and Control....Pages 113-121 Affine Poisson Structures in Analytical Mechanics....Pages 123-129 Front Matter....Pages 131-131 Quantum Frames, Quantization and Dequantization....Pages 133-145 Group Contractions and Stratonovich-Weyl Kernels....Pages 147-153 From Quantum Mechanics to Classical Mechanics and Back, via Coherent States....Pages 155-163 Inönü-Wigner Contraction of Kinematical Group Representations....Pages 165-173 A Coherent State Associated with Shape-Invariant Potentials....Pages 175-182 Front Matter....Pages 131-131 Quantization, Curvature and Temperature: The de Sitter Universe....Pages 183-190 Phase Coherent Wavelets, Fourier Transform, Magnetic Resonance Imaging, and Synchronized Time-Domain Neural Networks....Pages 191-204 Riccati Equation Over Torus and Semiclassical Quantization of Multiperiodic Motion....Pages 205-210 Front Matter....Pages 211-211 Hamiltonian Dynamics of Massless Objects....Pages 213-221 Quantum Magnetic Top....Pages 223-229 Quantum Mechanics on Z M and q -Deformed Heisenberg-Weyl Algebras....Pages 231-235 Stochastic Aspects of the Quantum Dynamics....Pages 237-244 Nonlinear Quantum Mechanics, the Separation Property, and a Stochastic Alternative to Certain Nonlinear Schrödinger Equations....Pages 245-255 Transitional Currents for Massive Spin One-Half Particles....Pages 257-263 Twisting Poincaré Algebras....Pages 265-271 On Poles of the Analytic Continuation of Integral Curves of a Family of Ordinary Differential Equations....Pages 273-275 A Covariant Approach to the Kustaanheimo-Stiefel Bundle in the Magnetic Monopole Theory....Pages 277-285 Back Matter....Pages 287-290