Quantum Theory and Symmetries: Proceedings of the Second International Symposium, Kraków, Poland, 18 – 21 July 2001

Description

This book presents the up-to-date status of quantum theory and the outlook for its development in the 21st century. The covered topics include basic problems of quantum physics, with emphasis on the foundations of quantum theory, quantum computing and control, quantum optics, coherent states and Wigner functions, as well as on methods of quantum physics based on Lie groups and algebras, quantum groups and noncommutative geometry. CONTENTS Preface Plenary Lectures The Interacting Fock Space of Haldane's Exclusion Statistics Complex Hamiltonians Having Real Spectra From Resonances to Poincare Semigroups Quantum Field Theory as Dynamical System Beta-Lattices for Aperiodic Order Generalized Symmetries and Time Integrable Hierarchies and the WDVV-equations Global Gauss Law for Lattice QCD Quantum Entanglement and Symmetries From Nonconunutative Space-time to Quantum Relativistic Symmetries with Fundamental Mass Parameter Tomographic Map within the Framework of Star-product Quantization Algorithmic Cooling and Scalable Quantum Computers: Ways to Improve the Space-time Requirements of the Algorithm Quantum Theory on the Torus with Magnetic Field Nonlocal Reflection by Photonic Barriers Lightfront Formalism versus Holography & Chiral Scanning Broken Symmetries Gauge Theories on Non-commutative Spaces Contributions Algebra of Differential Forms with Exterior Differential d3=0 in Dimension One Quantum Probability and the Non-locality Issue in Quantum Theory On the Electromagnetic Reciprocity-like Theorems Intertwining Operators for Schrodinger Algebras and Hierarchy of Invariant Equations Symmetries and Reduced Systems of Bethe Equations Construction of Wavelets Basis for the Fibonacci Chain via the Spline Functions of Various Orders Algebraic Model of Molecular Thermodynamics Induced Representations of Bicrossproduct Algebras Separation of Discrete Variables in the 2-dim Finite Oscillator Contractions of the Finite Oscillator A Glimpse at Mathematical Diffraction Theory Exactly Solvable Hamiltonians Connected with suq(2) and Quantum Optical Models Dynamical Coalgebra Symmetry and Integrability TTpw Vertex in Nuclear Matter Unusual Eigenvalue Problems Electroweak Interaction Fermions and Vector Bosons from Gauge and Space-time Symmetry Unification In Search of Alternatives to Higgs Fields Q-Plane Wave Solutions of q-Maxwell Equations Symmetries and Wavelets On Interpretations and Constructions of Classical Dynamical r-matrices Decoupling of Translations from Homogeneous Transformations in Inhomogeneous Quantum Groups Symmetries in the Universe at Large Scales From Geometry to Quantum Computation Partition Function Zeros of Aperiodic Ising Models Cayley-Klein Contractions of Orthosymplectic Superalgebras Distinguished Bases of sl(n C) and their Symmetries Quantum Effects in Matter-Wave Diffraction Time-type Quantum Deformation of the Conformal Algebra so(4 2) q-Laplace Operator Related to the Quantum Unitary Group Contraction and Interbases Expansions on N-sphere Quantized Symmetrizations and *-Products Uniqueness Results by Covariance in Covariant Quantum Mechanics Waves and Solitons in Born-Infeld Electrodynamics Quasiperiodic Patterns in Faraday Instability and Adapted Beta-Lattice On the SU(2) Wigner Function Dynamics VI Hilbert's Problem Infinite Lie Groups and Relativistic Physics On the Uncertainty Relations and Squeezed States for a Quantum Particle on a Circle Effective Dipole-type Field Approach and the Dual Higgs Model CP Violation in B Decays: The Role of Final-state Interactions Spinor Algebras and Extended Superconformal Algebras Wavelets and Tomograms in Information Processing Spectral Triples for the Kronecker Foliation Non-commutative Space-time Geometry and Principle of Gauge Invariance An Integrable Relativistic Three Body Problem with Spin and an Application Representations of SO0(P+1 q) x sRp+q+1 from its Deformations Covariance Approach to Quantum Theory Super Duffin-Kemmer-Petiau Algebra Deformed Jacobson Generators of the Algebra Uq[sl{n + 1)] and their Fock Representations Coherent States from Combinatorial Sequences Generalized Coherent States Associated with the CA-Extended Oscillator Asymmetric Double Sinh-Gordon Theory in 1+1 Dimensions Quantum Field Theory in Absence of the Positivity Condition On the Gauge Orbit Space Stratification Group-theoretical Aspects of Control of Quantum Systems Can the Breaking of Time-reversal Symmetry Introduce Bifurcations in Quantum Mechanics? Looking for a Time Operator Quantum and Classical Models Based on GL(n)-symmetry Q-boson Realization of the Positive Discrete Series of Representations of the Uq(2 1) Quantum Algebra Isotropic Quantized Minkowski Space and Poincare Group Construction of Raising and Lowering Operators for Uq(sl(2 R)) Exactly Solvable Time-dependent Potentials in Quantum Mechanics Representations for Selected Types of Diffusion Systems Quantum Mechanics at the Planck Scale Generalized PT Symmetry