9789810248871

Quantum Theory and Symmetries: Proceedings of the 2nd International Symposium Held in Krakow, Poland 18 - 21 July 2001

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  • ISBN13:

    9789810248871

  • ISBN10:

    9810248873

  • Format: Hardcover
  • Copyright: 2002-07-01
  • Publisher: WORLD SCIENTIFIC PUB CO INC

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Summary

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.

Table of Contents

Preface
The Interacting Fock Space of Haldane's Exclusion Statisticsp. 1
Complex Hamiltonians Having Real Spectrap. 11
From Resonances to Poincare Semigroupsp. 20
Quantum Field Theory as Dynamical Systemp. 43
Beta-Lattices for Aperiodic Orderp. 55
Generalized Symmetries and Timep. 66
Integrable Hierarchies and the WDVV-equationsp. 74
Global Gauss Law for Lattice QCDp. 96
Quantum Entanglement and Symmetriesp. 106
From Noncommutative Space-time to Quantum Relativistic Symmetries with Fundamental Mass Parameterp. 117
Tomographic Map within the Framework of Star-product Quantizationp. 126
Algorithmic Cooling and Scalable Quantum Computers: Ways to Improve the Space-time Requirements of the Algorithmp. 134
Quantum Theory on the Torus with Magnetic Fieldp. 144
Nonlocal Reflection by Photonic Barriersp. 160
Lightfront Formalism versus Holography&Chiral Scanningp. 165
Broken Symmetriesp. 183
Gauge Theories on Non-commutative Spacesp. 187
Algebra of Differential Forms with Exterior Differential d[superscript 3] = 0 in Dimension Onep. 198
Quantum Probability and the Non-locality Issue in Quantum Theoryp. 206
On the Electromagnetic Reciprocity-like Theoremsp. 212
Interwining Operators for Schrodinger Algebras and Hierarchy of Invariant Equationsp. 222
Symmetries and Reduced Systems of Bethe Equationsp. 228
Construction of Wavelets Basis for the Fibonacci Chain via the Spline Functions of Various Ordersp. 235
Algebraic Model of Molecular Thermodynamicsp. 243
Induced Representations of Bicrossproduct Algebrasp. 249
Contractions of the Finite Oscillatorp. 255
Separation of Discrete Variables in the 2-dim Finite Oscillatorp. 261
A Glimpse at Mathematical Diffraction Theoryp. 267
Exactly Solvable Hamiltonians Connected with su[subscript q](2) and Quantum Optical Modelsp. 273
Dynamical Coalgebra Symmetry and Integrabilityp. 279
[pi][rho][omega] Vertex in Nuclear Matterp. 285
Unusual Eigenvalue Problemsp. 291
Electroweak Interaction, Fermions and Vector Bosons from Gauge and Space-time Symmetry Unificationp. 305
In Search of Alternatives of Higgs Fieldsp. 311
q-Plane Wave Solutions of q-Maxwell Equationsp. 318
Symmetries and Waveletsp. 324
On Interpretations and Constructions of Classical Dynamical r-matricesp. 331
Decoupling of Translations from Homogeneous Transformations in Inhomogeneous Quantum Groupsp. 337
Symmetries in the Universe at Large Scalesp. 343
From Geometry to Quantum Computationp. 348
Partition Function Zeros of Aperiodic Ising Modelsp. 354
Cayley-Klein Contractions of Orthosymplectic Superalgebrasp. 360
Distinguished Bases of sl(n,C) and their Symmetriesp. 366
Quantum Effects in Matter-Wave Diffractionp. 371
Time-type Quantum Deformation of the Conformal Algebra so(4,2)p. 377
q-Laplace Operator Related to the Quantum Unitary Groupp. 383
Contraction and Interbases Expansions on N-spherep. 389
Quantized Symmetrization and *-Productsp. 396
Uniqueness Results by Covariance in Covariant Quantum Mechanicsp. 404
Waves and Solitons in Born-Infeld Electrodynamicsp. 412
Quasiperiodic Patterns in Faraday Instability and Adapted Beta-Latticep. 425
On the SU(2) Wigner Function Dynamicsp. 431
VI Hilbert's Problem, Infinite Lie Groups and Relativistic Physicsp. 437
On the Uncertainty Relations and Squeezed States for a Quantum Particle on a Circlep. 444
Effective Dipole-type Field Approach and the Dual Higgs Modelp. 449
CP Violation in B Decays: The Role of Final-state Interactionsp. 456
Spinor Algebras and Extended Superconformal Algebrasp. 463
Wavelets and Tomograms in Information Processingp. 473
Spectral Triples for the Kronecker Foliationp. 481
Non-commutative Space-time Geometry and Principle of Gauge Invariancep. 487
An Integrable Relativistic Three Body Problem with Spin and an Applicationp. 492
Representations of SO[subscript 0](p + 1,q) x[subscript s] R[superscript p+q+1] from its Deformationsp. 504
Covariance Approach to Quantum Theoryp. 511
Super Duffin-Kemmer-Petiau Algebrap. 517
Deformed Jacobson Generators of the Algebra U[subscript q][sl(n+1)] and their Fock Representationsp. 521
Coherent States from Combinatorial Sequencesp. 527
Generalized Coherent States Associated with the C[subscript [lambda]]-Extended Oscillatorp. 531
Asymmetric Double Sinh-Gordon Theory in 1+1 Dimensionsp. 537
Quantum Field Theory in Absence of the Positivity Conditionp. 547
On the Gauge Orbit Space Stratificationp. 553
Group-theoretical Aspects of Control of Quantum Systemsp. 559
Can the Breaking of Time-reversal Symmetry Introduce Bifurcations in Quantum Mechanics?p. 568
Looking for a Time Operatorp. 574
Quantum and Classical Models Based on GL(n)-symmetryp. 582
q-boson Realization of the Positive Discrete Series of Representations of the U[subscript q](2,1) Quantum Algebrap. 589
Isotropic Quantized Minkowski Space and Poincare Groupp. 595
Construction of Raising and Lowering Operators for U[subscript q](sl(2,R))p. 601
Exactly Solvable Time-dependent Potentials in Quantum Mechanicsp. 607
Representations for Selected Types of Diffusion Systemsp. 615
Quantum Mechanics at the Planck Scalep. 621
Generalized PT Symmetryp. 626
Table of Contents provided by Blackwell. All Rights Reserved.

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