Ebook: Group Theoretical Methods in Physics: Proceedings of the XVI International Colloquium Held at Varna, Bullgaria, June 15–20, 1987

The aim of this well-known annual colloquium on group theoretical and geometrical methods in physics is to give an overview of current research. Original contributions along with some review articles cover relevant mathematical developments as well as applications to physical phenomena. The volume contains contributions dealing with concepts from classical group theory, supergroups, superalgebras, infinite dimensional groups, Kac-Moody algebras and related structures. Applications to physics include quantization methods, nuclear physics, crystallography, gauge theory and strings in particle physics. Most of the articles have an introductory or a review section, so the volume will be useful not only for researchers but also for graduate students.

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The aim of this well-known annual colloquium on group theoretical and geometrical methods in physics is to give an overview of current research. Original contributions along with some review articles cover relevant mathematical developments as well as applications to physical phenomena. The volume contains contributions dealing with concepts from classical group theory, supergroups, superalgebras, infinite dimensional groups, Kac-Moody algebras and related structures. Applications to physics include quantization methods, nuclear physics, crystallography, gauge theory and strings in particle physics. Most of the articles have an introductory or a review section, so the volume will be useful not only for researchers but also for graduate students.
Content:
Front Matter....Pages -
Horospheres and Twistors....Pages 1-10
Spectrally ordered Lie algebras....Pages 11-16
Algebraic expressions for classes of generalized 6-j and 9-j symbols for certain Lie groups....Pages 17-34
Harmonic analysis on coset spaces....Pages 35-42
The mapping class group: Homology and linearity....Pages 43-51
Invariantly ordered spectral lie algebras as abstract dynamical systems....Pages 52-56
Realizations of representations of Kac-Moody groups and bilinear equations for τ-functions....Pages 57-64
Recent developments in non linear representations and evolution equations....Pages 65-73
New constructions for representations of semisimple lie groups....Pages 74-88
Nonrelativistic supersymmetry....Pages 89-96
Superfield algebraic structures with Grassmann-valued structure constants....Pages 97-103
The non-uniqueness of supertrace....Pages 104-108
Cohomological methods in supermanifold theory....Pages 109-115
Superalgebras of symmetries in superquantum mechanics....Pages 116-125
Supersymmetric quantum mechanics and critical potentials....Pages 126-141
Constrained lagrangians in N = 2-superspace formulations for the constant magnetic field system....Pages 142-148
On some graded algebras....Pages 149-153
Self-consistency and supersymmetry in a many fermion system....Pages 154-160
Essentially irreducible representations of the lie superalgebras sl(n/1) and sl(n/2)....Pages 161-168
Octonions without octonions....Pages 169-175
Soliton solutions and bilinear residue formula for the super Kadomtsev-Petviashvili hierarchy....Pages 176-184
Indices for plethysms of representations of Lie superalgebras....Pages 185-189
Constructions of Lie (super)algebras from triple systems....Pages 190-197
Coherent states and quantization on homogeneous spaces....Pages 199-207
Relativistic spectrum generating groups: Spectrum and radiative transitions in a collective model for hadrons....Pages 208-222
Heisenberg equations of motion for, the Coulomb problem and so(4.2)....Pages 223-229
Degenerate representations from quantum kinematical constraints....Pages 230-237
Application of non-bijective transformations to various potentials....Pages 238-244
Nonuniqueness of the variational formulation of classical equations of motion and quantization rules....Pages 245-249
About Quadratic Transformations Connected To Hurwitz Transformations....Pages 250-252
Geometric quantization of Riemann ellipsoids....Pages 253-260
Group-theoretic approach to scattering: The Dirac-Coulomb problem and relativistic supersymmetry....Pages 261-267
On a quantum mechanical d'Alembert principle....Pages 268-274
Geometric quantization of the Kepler problem with a magnetic charge....Pages 275-281
Lie algebra of a derivative nonlinear Schrödinger equation....Pages 282-288
Symmetry and classification of energy bands in crystals....Pages 289-308
Dynamical su(8) for phase-coexistence: Thermodynamics of an so(4) × so(4) submodel....Pages 309-314
Chain adaptation of space group representations and induced space group Clebsch-Gordan matrices....Pages 315-321
Perturbation of bisemigroups and transport theory....Pages 322-325
Space group representations induced by local site symmetries....Pages 326-333
Quasicrystals: A distanced overview....Pages 334-343
The time inversion symmetry in case of time translation existing....Pages 344-346
Ergodic properties of hard rod systems....Pages 347-351
Reducible space groups....Pages 352-356
Colour space groups of all cubic chromomorphic classes and their application....Pages 357-362
Auxiliary group approach for group-subgroup related transformation matrices....Pages 363-369
A new approach to non-periodic order in solids....Pages 370-376
Group theoretical analysis of the lattice distorsion in anisotropic Superconductivity....Pages 377-382
The topological theory of semidefects....Pages 383-398
Symmetries in nuclei....Pages 399-407
Boson representation of Sp(24, R) and classification of even-even nuclei....Pages 408-413
Group Theory of the Symplectic Nuclear Model....Pages 414-422
The nuclear collective WSp(6,R) model....Pages 423-428
Extension of the interacting boson model: Higher order interactions preserving the dynamical symmetry (The 0(6) limit)....Pages 429-433
Classical Yang-Mills fields with non-compact invariance....Pages 435-444
Cartan connections in conformal gauge theories....Pages 445-455
The anomaly-flux-index identity and its Euclidean extension....Pages 456-469
Quantization of anomalous gauge theories: The chiral Schwinger model....Pages 470-476
QED as a theory of quantized connection forms....Pages 477-484
Group-theoretical aspects of dimensional reduction....Pages 485-497
The symmetry group of the Euclidean CPn model as the invariance group of two bilinear formst....Pages 498-503
Complex scalar fields in SO(2,1)-Invariant backgrounds: Representation of the symmetries in the schrödinger picture....Pages 505-512
Conformally invariant wave equations on 3+2 de sitter space....Pages 513-514
Massless particles in de sitter space....Pages 515-522
Covariant lagrangian formulation of interacting heterotic strings....Pages 523-529
A generalization of the fourier transform and applications to quantum field theory....Pages 530-536
Harmonic representatives of instantons and self-dual monopoles....Pages 537-543
Homogeneous space construction of Modular Invariant QFT models with a chiral U(1) current....Pages 544-547
Some solutions of the U(N) sigma models....Pages 548-554
Fermions and Jordan matrices....Pages 555-568
Algebraic and arithmetic geometry in string theory....Pages 569-574
....Pages 575-586