GROUP 24: Physical and Mathematical Aspects of Symmetries: Proceedings of the 24th International Colloquium on Group Theoretical Methods in Physics, Paris, 15-20 July 2002

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ISBN: 9780750309332 | 0750309334
Cover: Hardcover
Copyright: 11/30/2003

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One of the most enduring elements in theoretical physics has been group theory. GROUP 24: Physical and Mathematical Aspects of Symmetries provides an important selection of informative articles describing recent advances in the field. The applications of group theory presented in this book deal not only with the traditional fields of physics, but also include such disciplines as chemistry and biology. Awarded the Wigner Medal and the Weyl Prize, respectively, H.J. Lipkin and E. Frenkel begin the volume with their contributions. Plenary session contributions are represented by 18 longer articles, followed by nearly 200 shorter articles. The book also presents coherent states, wavelets, and applications and quantum group theory and integrable systems in two separate sections. As a record of an international meeting devoted to the physical and mathematical aspects of group theory, GROUP 24: Physical and Mathematical Aspects of Symmetries constitutes an essential reference for all researchers interested in various current developments related to the important concept of symmetry.

Foreword	p. v
Introduction	p. ix
International Standing Committee	p. x
International Advisory Committee	p. x
Local Organizing Committee	p. xi
Obituary	p. xiii
The 2002 Wigner Medal	p. 1
The Wigner Medal 2002: Introduction	p. 3
Awarding of the Wigner Medal for 2002 to Prof H J Lipkin of the Weizmann Institute of Science Rehovoth, Israel	p. 5
Response to the award of the Wigner Medal	p. 7
The 2002 Hermann Weyl Prize	p. 15
The Hermann Weyl Prize: Introduction	p. 17
Affine Kac-Moody algebras, integrable systems and their deformations	p. 21
Plenary Sessions	p. 33
Quantum computing using dissipation	p. 33
Properties of non-Hermitian quantum field theories	p. 43
Cooperativity and symmetry at biological scales	p. 51
Quantum geometry of ADE diagrams and generalized Coxeter-Dynkin systems	p. 61
A review of Berezin--and other--quantization methods	p. 73
Symmetry and graph theory as tools for the treatment of [pi]-systems	p. 81
Noncommutative geometry and physics: the first 10 years	p. 89
Delone set models for quasicrystals	p. 99
Lie symmetries for lattice equations	p. 103
Path group in gauge theory and gravity	p. 113
Recent applications of topology and group theory in condensed matter	p. 121
Exceptional groups and physics	p. 129
Group projection method in statistical systems	p. 139
Symmetric polynomials in physics	p. 147
Strings, symmetries and representations	p. 153
Solitons, platonic symmetry and Fullerenes	p. 161
Special Plenary Session & Round Table: Historical and Epistemological Aspects of Group Theory in Physics	p. 169
Historical and epistemological aspects of group theory in physics: An interlude	p. 171
What if Einstein had not been there? A Gedankenexperiment in science history	p. 173
Discrete Groups and Geometry	p. 183
Wavelet basis for quasicrystal diffraction	p. 185
Haar wavelets for the quasiperiodic icosahedral Danzer tiling	p. 189
Quasicrystalline combinatorics	p. 193
Self-similar cut-and-project sequences	p. 201
Closed geodesics in cosmology and discrete group actions on hyperbolic manifolds	p. 205
Using the renormalization group for the evaluation of electronic localization	p. 209
Tilings and coverings embedded into the canonical decagonal tiling T*[superscript (A subscript 4)]	p. 213
Delone sets of beta-integers, Rauzy fractals and adeles	p. 219
Superspace groups for incommensurate composite systems	p. 223
Strings, Cosmology and Gravitation	p. 227
Spacetime algebraic skeleton	p. 229
Are we permitted to deform the Poincare group?	p. 233
O(d+1,d+n+1)-invariant formulation of stationary heterotic string theory	p. 237
Metric-polynomial structures and gravitational Lagrangians	p. 241
Octonions and M-theory	p. 245
Symmetry and invariance in Leibniz's approach of natural phenomena. Application to dynamics	p. 249
Gravitating lumps--2002	p. 255
Group theoretical approach to QFT in de Sitter space	p. 263
Time in quantum geometrodynamics	p. 267
Conformal Lie algebras of spacetimes	p. 271
Orthogonal symmetry and matrix potentials in heterotic string theory	p. 275
Orthogonal polynomials of several discrete variables and the 3nj-Wigner symbols: applications to spin networks	p. 279
Holomorphic realization of non-commutative space-time and gauge invariance	p. 283
Four classes of modified relativistic symmetry transformations	p. 287
Cosmic evolution as inertial motion in the field space of GR	p. 293
New Einstein-Hilbert type action and unity of nature	p. 297
Fuzzy D-branes on group manifolds	p. 301
Fractals in cosmology	p. 305
Quantization of scalar fields in curved background, deformed Hopf algebra and entanglement	p. 309
Conformal Theories and Integrable Systems	p. 313
Generalized non-abelian Toda models of dyonic type	p. 315
Local scale invariance, conformal invariance and dynamical scaling	p. 319
Loop models from Coulomb gases and supersymmetry: Goldstone phases in 2D polymers	p. 323
Magnetic properties of quasi-one-dimensional strongly correlated systems	p. 327
Joint description of periodic SL(2,R) WZNW model and its coset theories	p. 331
Particle and Nuclear Physics	p. 335
Representations and interactions from field equations on an extended spin space	p. 337
Mass relations for the quark-diquark model	p. 341
On the role of quantum deformation in isovector pairing interactions in nuclei	p. 347
Mixed-symmetry shell-model calculations	p. 351
The boson/fermion statistic for SU(3) colour requires quark confinement	p. 355
How to define colour charge in quantum chromodynamics	p. 359
Geometrisation of electromagnetic and weak interactions and geometrical mechanism of P and T violation	p. 363
Weak chiral symmetry in the standard model--deformed cyclic symmetry for chiral family mixings	p. 367
Stability of monopole condensation in SU(2) QCD	p. 371
Atomic and Molecular Physics, Theoretical Chemistry, Condensed Matter	p. 377
Algebraic models and quantum deformations in molecular thermodynamics	p. 379
The Bilbao Crystallographic Server	p. 383
Quantum algebraic symmetries in atomic nuclei and metal clusters	p. 387
Broken symmetry and symmetry classification of magnetic ordering in doped crystals	p. 391
Duality and conformal twisted boundaries in the Ising model	p. 395
Quantum Frenkel-Kontorova model	p. 399
Geometric mechanics for applications in diatomic and triatomic molecular dynamics	p. 403
Regular fractal structure of the energy matrix in 1D Heisenberg open spin-1/2 chains	p. 409
New applications of the group theory in the kinetic theory of gases	p. 413
Ladder operators for integrable one-dimensional lattice models	p. 417
Macroscopic properties of A-statistics and A-superstatistics	p. 421
Admissible partitions and the square of the Vandermonde determinant	p. 425
Noncommutative Geometry	p. 429
Yang-Mills and Born-Infeld actions on finite group spaces	p. 431
Noncommutative geometry on the algebra U(su[subscript 2]) and quantization of coadjoint orbits	p. 435
Quantum de Rham complex with d[superscript 3] = 0 differential on GL[subscript p,q](2)	p. 439
Realization of q-deformed spacetime as star product by a Drinfeld twist	p. 443
Equivariant noncommutative index on braided orbits	p. 447
Noncommutative planar particles: higher order versus first order formalism and supersymmetrization	p. 451
A locally trivial quantum Hopf bundle	p. 455
Z[subscript n]-graded topological generalizations of supersymmetry and orthofermion algebra	p. 459
Homogeneous algebras, parastatistics and combinatorics	p. 463
Lie algebras of order F and extensions of the Poincare algebra	p. 469
Noncommutative differential geometric method to fractal geometry	p. 473
Non-commutative standard model	p. 477
Methods and Applications of Quantum Theory	p. 481
65th Birthday Tribute to Allan Solomon	p. 483
Dissipative 'groups' and the Bloch ball	p. 485
Gauging quantum-mechanical space-time symmetry	p. 489
Quantum XOR operation using macroscopic polarization states of light in Mach-Zehnder interferometer	p. 493
Semigroup techniques for the efficient classical simulation of optical quantum information	p. 497
Groups and semigroups in scattering theory--Poincare transformations and decaying states	p. 501
Quantum ground-mode computation with static gates	p. 511
Complex coherent states and non equilibrium quantum thermodynamics	p. 515
Deformation quantization of damped systems	p. 519
Coherent state realizations of su(n + 1) in terms of subgroup functions	p. 523
Metric formulation of Galilean invariance in five dimensions	p. 527
Nonperturbative approach to potentials in impenetrable boxes based on quasi-exact solvability	p. 531
Critical temperature for entanglement transition in Heisenberg Models	p. 535
Nonlinear extension of quantum mechanics: remarks and recent results	p. 539
Quantization of the linearized Kepler problem	p. 545
Alternative Hamiltonians and Wigner quantization	p. 549
Spectral properties of Landau operator with [delta] cylinder interaction	p. 553
The Jaynes-Cummings model and raising and lowering operators	p. 557
Differential form of the star product for SU(2) Stratonovich-Weyl symbols	p. 561
On the combined effect of different symmetries on quantum mechanical potentials	p. 565
The application of Lie algebras to the separation of degrees of freedom in problems with many degrees of freedom	p. 569
Multivariable Hermite polynomials, nonlinear coherent states and photon distributions	p. 573
Hidden SL(2,R) symmetry for time-dependent Schrodinger equations	p. 577
The particle-operator and particle states in quantum field theory	p. 581
Combinatorics of boson normal ordering: the Dobinski formula revisited	p. 585
Non-Hermitian Hamiltonians with real and complex eigenvalues: An sl(2,C) approach	p. 589
The stationary Maxwell-Dirac equations	p. 593
Confined systems through variational supersymmetric quantum mechanics	p. 597
Quantum version of Hamilton-Jacobi theory for time-dependent systems	p. 601
Heun equation and Inozemtsev models	p. 605
Group-theoretical and algebraic aspects of Bose-Einstein condensation of interacting particles in traps	p. 609
Quantum coding with systems with finite Hilbert space	p. 613
A note on the optimal teleportation	p. 617
Generalized relativistic dynamics as a dynamics of third order	p. 621
Reorganization of energy bands in quantum finite particle systems	p. 625
PT symmetry and supersymmetry	p. 629
Algebras, Groups and their Representations	p. 633
New infinite-dimensional Lie algebras of U (N[subscript +], N[subscript -])-tensor operators and applications	p. 635
Invariants of Lie algebras having a frobeniusian structure	p. 639
Quantization on compact groups	p. 643
Special functions, raising and lowering operators	p. 649
All positive energy UIRs of D=6 conformal supersymmetry	p. 653
Supersymmetry and special functions	p. 657
Quantization of phases and moduli in terms of the group SO[superscript up arrow] (1, 2)	p. 661
p-Mechanical brackets and method of orbits	p. 665
The Kahler form on the loop group and the Radul cocycle on pseudo-differential operators	p. 671
Cohomology and Bessel functions theory	p. 677
Representations of classical Lie algebras from their quantum deformations	p. 683
On the symmetries of the 16 Genetic Code-Doublets	p. 687
A group theoretical approach to quantum theories on commutative and non-commutative spheres	p. 691
Milne phase for the Coulomb quantum problem related to Riemann's hypothesis	p. 695
Hierarchy of gradings on sl(3, C) and summary of fine gradings on sl(4, C)	p. 699
Quadratic algebras in simple exclusion models	p. 703
Finite su(2)-oscillator; applications to signal processing	p. 707
Nonlinear Systems and their Symmetries	p. 711
Infinite-dimensional Lie groups of symmetries of the ideal MHD equilibrium equations	p. 713
Lie symmetries of nonlinear reaction-diffusion systems with variable diffusivities	p. 717
On geometric aspects of Weierstrass representations associated with CP[superscript N] harmonic maps	p. 721
Integrability and exact solution of an electronic model with long range interactions	p. 725
Conservation laws for fractional differential equations	p. 729
A new powerful method for solving non-linear differential equations: Burgers' equation as an example	p. 733
On infinite symmetries and essential conservation laws for Navier-Stokes equations	p. 737
Green's function for dissipative quantum systems and its relation to nonlinear evolution equations	p. 741
On the role of weak transversality in Lie group theory	p. 747
Mini-Symposium: Quantum Group Theory and Integrable Systems Invited Talks	p. 751
q-Painleve systems arising from a q-difference analogue of the KP hierarchy	p. 753
On constructions of Fock Space	p. 755
Representations of quantum groups: constructions and characters from a Hopf algebraic point of view	p. 757
On examples of locally compact quantum groups	p. 759
Haar weight on some quantum groups	p. 763
Mini-Symposium: Quantum Group Theory and Integrable Systems Contributions	p. 773
RTT presentation of ortho-symplectic super Yangians. Quasi-Hopf deformation	p. 775
Integrable models with comodule algebra symmetry	p. 779
Topological invariants of three-manifolds from U[subscript q](osp(1[vertical bar]2n))	p. 783
Quantum groups and interacting quantum fields	p. 787
Dirac monopoles from the Matsumoto non-commutative spheres	p. 791
Q-Boson realization of the quantum algebras	p. 795
Dynamical systems associated to bicrossproducts	p. 799
Combinatorics of the q-shuffle product and the quon Weyl algebra	p. 803
Decoupling of tensor factors in cross product and braided tensor product algebras	p. 807
Differential calculus on quantum spaces	p. 811
On generalized Freudenthal-Kantor triple systems and Yang-Baxter equations	p. 815
The Jordanian bicovariant differential calculus	p. 819
Differential calculus on a novel cross-product quantum algebra	p. 823
q-deformations of classical (and quantum) integrable systems associated with coalgebras	p. 827
Sum rules for codon usage frequencies	p. 833
About rational-trigonometric deformation	p. 837
Satellite Colloquium: Coherent States, Wavelets and Signal Processing	p. 843
Coherent states, wavelets and applications	p. 844
Coherent States and Phase Space Methods	p. 845
Symplectic geometry of the Wigner transform on noncompact symmetric spaces	p. 847
Wavelet transform and [star] exponential	p. 855
Phase space techniques for the study of generalized Anti-Wick operators	p. 863
Admissible vectors and traces on the commuting algebra	p. 867
Localization of frames	p. 875
Lattices of coherent states and square integrability	p. 883
Unified view of tomographic and other transforms in signal analysis	p. 887
Wavelets and their Applications	p. 891
Wavelet based regularization for Euclidean field theory	p. 893
Measuring a curvature radius with directional wavelets	p. 899
Extracting structural and dynamical informations from wavelet-based analysis of DNA sequences	p. 905
Deficient splines wavelets	p. 915
A general recurrence relation between the moments of a scaling function	p. 921
Atom modulus quantization for matching pursuits	p. 925
Multiscale observations of the solar atmosphere	p. 931
Wavelet transform associated to a homogeneous Siegel domain	p. 937
Modeling 2D+1 textures	p. 943
An application of space-adaptive lifting: Image retrieval	p. 949
Hybrid audio models and transform coding	p. 953
A wavelet-based model for forecasting non-stationary processes	p. 955
Louvain-la-Neuve Satellite Workshop List of participants	p. 959
Group 24 in Paris List of participants	p. 961
Author index	p. 965
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GROUP 24: Physical and Mathematical Aspects of Symmetries: Proceedings of the 24th International Colloquium on Group Theoretical Methods in Physics, Paris, 15-20 July 2002

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