Group Theoretical Methods in Physics: Proceedings of the XVIII International Colloquium Held at Moscow, USSR, 4–9 June 1990

M. A. Markov (auth.), Victor V. Dodonov, Vladimir I. Man’ko (eds.)3540540407, 9783540540403, 0387540407

This volume contains review talks and a small selection of the research papers presented at the world’s most distinguished conference on group theoretical methods in physics. The papers are devoted to such topics as spectrum generating groups, quantum groups, coherent states, and geometric aspects of group representations. The methods apply to nuclear physics, quantum mechanics, ordinary and supersymmetric linear and non- linear differential equations, geometry, and non-commutative geometry. The book addresses theoretical physicists, especially those in research.

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Table of contents :
Introductory talk….Pages 3-4
Creating “clouds”….Pages 5-15
Opening remarks….Pages 19-19
Laudatio for Professor Francesco Iachello….Pages 20-21
Symmetry….Pages 22-31
Dynamical and fundamental symmetries in particles and nuclei….Pages 35-62
Spectrum generating groups — idea and application….Pages 63-84
The role of dynamic symmetries and supersymmetries in nuclear physics….Pages 85-97
SO(3,2) for oscillator and hydrogenlike systems….Pages 98-105
Conformal groups in the Kepler problem….Pages 106-110
Potential group in optics: The maxwell fish-eye system….Pages 111-119
Transition to chaos in hadronic systems….Pages 120-123
The dynamical group of Riemann ellipsoids….Pages 124-127
An algebraic model of cluster states in odd-mass nuclei….Pages 128-131
Compact to noncompact transition and nuclear collective levels….Pages 132-135
$$overline {SL(3,R)} times T^6$$ as a nuclear collective motion group….Pages 136-139
Exceptional groups and the interacting boson approximation….Pages 140-143
An overview of quantum groups….Pages 147-163
Integrable theories, Yang-Baxter algebras and quantum groups: An overview….Pages 164-176
Finite – dimensional irreducible representations of the quantum superalgebra Uq[gl(n/I)]….Pages 177-182
Projection operator method and Q-analog of angular momentum theory….Pages 183-194
Quantum algebras and symmetries of dynamical systems….Pages 195-198
Coulomb gas realization of simple quantum groups….Pages 199-203
String theory, quantum gravity and quantum groups….Pages 204-207
q -Oscillator realizations of the quantum superalgebras sl q (m, n) and osp q (m, 2n) ….Pages 208-214
Relativistic oscillator = q -oscillator….Pages 215-220
Some aspects of the angular momentum coefficients in SU q (2)….Pages 221-224
Contractions and analytic continuations of the irreducible representations of the quantum algebra su q (2)….Pages 225-228
Universal R-matrix for quantum supergroups….Pages 229-232
Recent progress in non-commutative geometry….Pages 233-240
Algebraic gauge theory and noncommutative geometry….Pages 241-248
Classification of the symmetries of ordinary differential equations….Pages 251-262
Conditional symmetries and conditional integrability for nonlinear systems….Pages 263-271
Cohomology and symmetry of differential equations….Pages 272-276
Derivations of semi-basic forms and symmetries of second-order equations….Pages 277-280
Hamilton-Jacobi equations in SU (2, 2) homogeneous spaces….Pages 281-284
Linearization of PDEs….Pages 285-288
Perturbed nonlinear equations: Application to the Korteweg-Devries equation considered as a perturbed Euler equation….Pages 289-293
Algebraic version of the soliton perturbation theory….Pages 294-298
Extended chiral conformal models with a quantum group symmetry….Pages 299-313
Conformal reduction of WZNW theories and W-algebras….Pages 314-327
The resurrection of a forgotten symmetry: De broglie’ s symmetry….Pages 331-338
Relativistic invariance of a many body system with a Dirac oscillator interaction….Pages 339-345
Derivation of the geometrical berry phase….Pages 346-350
Gauge translations and the Berry phase….Pages 351-355
Geometric quantization: Regular representations and modular algebras….Pages 356-364
Geometro-stochastic quantization and quantum geometry….Pages 365-372
SO(4,1)-Coherent states and the geometro-stochastic quantization of a gauge theory for extended objects….Pages 373-378
Covariant quantum mechanics and the symmetries of its radiation fields….Pages 379-382
Double stratonovich – Hubbard trick and novel path integral for a system of interacting fermions….Pages 383-393
Nonrelativistic limit of superfield theories….Pages 394-398
Remarks on the supersymmetric WKB quantization formula….Pages 399-403
Particle in a self-dual monopole field: example of supersymmetric quantum mechanics….Pages 404-409
Supersymmetry and electron angular momentum….Pages 410-413
Parasupersymmetries and Lie superalgebras….Pages 414-417
Quantum chaos: Spectra and states….Pages 418-433
Quantum ergodicity and eigenvalue problems for plane polygons….Pages 434-437
“Classical” in terms of general statistical models….Pages 438-441
Temporal decoherence in Lorentz-squeezed hadrons….Pages 442-449
Physical significance of correlated and squeezed states….Pages 450-456
On the symmetry and dynamics of squeezed and correlated states….Pages 457-460
Correlated States of Quantum Chain….Pages 461-468
Interaction of weak coherent light with a system of two – level atoms in a lossless cavity….Pages 469-474
Time dependent quantum tunnelling….Pages 475-482
Non-spurious harmonic oscillator states with arbitrary permutational symmetry….Pages 483-486
Symmetry analysis of the qualitative intramolecular phenomena….Pages 487-489
Algebras of the SU(n) vector invariants and some of their applications….Pages 493-504
Product formulas for Q-representatives….Pages 505-507
Tensor products for affine Kac-Moody algebras….Pages 508-511
Atypical modules of the lie superalgebra gl (m/n) ….Pages 512-515
Vector coherent state theory of the non-compact orthosymplectic superalgebras….Pages 516-521
The composition factors of kac modules of sl(M/N) ….Pages 522-526
Clifford algebras, spinors and finite geometries….Pages 527-530
Reducibility of Euclidean motion groups….Pages 531-534
Software packages: Space groups and their representations….Pages 535-538
Software packages: Transformation coefficients for space groups….Pages 539-542
Icosahedral dissectable tilings from the root lattice D 6 ….Pages 543-547
Groups with G-number parameters….Pages 548-555
Regge Calculus with torsion….Pages 556-560
Quasiperiodicity: Local and global aspects….Pages 561-572
Derivative Moufang transformations….Pages 573-574
On the explicit form of consistent anomalies….Pages 575-580
Berry phases and Wyckoff positions for energy bands in solids….Pages 581-587
Crystallography of quasicrystals: The problem of restoration of broken symmetry….Pages 588-601