Group Theoretical Methods in Physics

Inhaltsverzeichnis

• Non-compact groups and irreducible representations.
• Duality theorems in conformal geometry.
• Covariant differential operators.
• Generalized young tableaux and weight multiplicity for classical Lie groups.
• G(2) ? SU(2) x SU(2) shift operators and scalars.
• Generalised young tableaux for Lie algebras and superalgebras.
• The DeSitter symmetry of the Dirac equation.
• Casimir operators for inhomogeneous classical groups.
• Construction and unitary representations of the non - compact groups of supergravity.
• A new look at group orthogonality relations.
• Lie supergroups and graded Lie groups.
• The invariants of the nondegenerate representations of the group of the pseudo — orthogonal matrices SO(P,1).
• Topological and algebraic structure of linear problems associated with completely integrable systems.
• Infinite dimensional symmetry algebras in integrable systems.
• Scattering and transfer in some group theoretical potentials.
• Reduction of supersymmetric ?-models on graded manifolds.
• Two dimensional ?-models and harmonic maps from S2 to S2n.
• Completely integrable Hamiltonian systems and the separation of variables.
• Conformally invariant pure spinor models.
• “Exact solvability in chiral and gauge theories”.
• An inverse scattering transform technique for stationary Axi-symmetric Einsteins-Maxwell fields.
• The symmetric space property and the embedding problem for stationary Axi-symmetric Einstein-Maxwell fields.
• Self-dual Yang-Mills as a totally integrable system.
• Constrained Hamiltonian systems.
• Backlund problem, differential algebra and group theory.
• Are atomic Hartree-Fock equations linearizable?.
• Oscillator-like unitary representations of non-compact groups and supergroups and extended supergravity theories.
• Gravity, supergravities and integrablesystems.
• Free graded differential superalgebras.
• Relativistic wave equations from supergroup quantization.
• Generalized Kerr-Schild transformation.
• Adding a ?-term to pp-wave solutions of the Einstein field equations.
• Aspects of a spin(1,4) gauge theory with Kaluza-Klein symmetry.
• Composite gravity and composite supergravity.
• Labelling of irreducible representations of super Lie algebras.
• Tensorial properties of incommensurate crystals.
• Bifurcations and symmetry changes in crystals.
• The structure of space — Groups'unitary representations.
• Band structure of almost periodic potentials.
• Space group representations for crystal structure types.
• Selection rules for polymers.
• Automorphism symmetries of space group selection rules.
• Invariant formulation for the zeros of covariant vector fields.
• Associated corepresentations and symmetry of Clebsch-Gordan coefficients.
• Generalized and symmetrized Clebsch Gordan coefficients for antiunitary groups.
• Generalized coupling coefficients for space groups.
• Active representations of space groups based on the cubic lattice.
• Reduced large N models.
• Derivation of infinite-component wave equations from field theory.
• Maximal symmetries on potentials and gauge invariance.
• Ghosts, Anomalies and the geometry of gauge fields.
• Colour algebras and generalized statistics.
• The branching rule of Weyl and the quantum number b(?1, ?2, ?3).
• On a new regularization method for Feynman diagrams.
• Explicit realization of E8.
• Dynamical symmetry breaking in SU(2) × U(1) in weak coupling limit.
• Dynamical unification of fermions and gauge bosons for internal symmetry and gravity.
• Q =I3 + 12Y. WHY?.
• Examples of group contraction.
• Symmetry breaking in the spectrum generating group and its experimental tests.
• Construction ofthe dynamical symmetry group of the relativistic harmonic oscillator by the Infeld-Hull factorization method.
• Dynamical semigroups for resonances in rigged Hilbert spaces.
• Extrema of Landau and Higgs polynomials and zeros of renormalization-group equations.
• Group contraction and macroscopic quantum systems.
• The Interacting Boson Model and its connection with group theory.
• Boson mappings in nuclear physics. A brief and prejudiced survey.
• Does accidental degeneracy imply a symmetry group?.
• “A hidden symmetry incollective excitations of many-body systems”.
• The U(6) symmetry in the microscopic collective model.
• SO(2n+1) in an [SU(2)]n basis: Symmetric representations.
• A formalism for the microscopic interacting boson model with non-degenerate orbits.
• SU(3) in an 0(3) basis: Eigenvalue spectrum of the Q l 0 AND O l 0 operators.
• SU(4) in an SO(4) basis : Shift operator technique.
• The algebraic geometry of multimonopoles.
• Dimensional reduction, spinor fielks and characteristic classes.
• Graded bundles in the Ogievetsky-Sokatchev supergravity.
• Analysis and comparison of different ways of identification of spin functions variables.
• A generalized imprimitivity theorem for a class of POV — measures.
• Inversions in twistor space.
• Physical group theory and Euclidean space.
• Some aspects of random walks on groups.
• Ising model on finitely presented groups.
• Self-triality in statistical mechanics and field theory.
• Symmetries of finite hard rod systems.
• Influences of lattice dimension d and character of spin-interactions on the thermodynamics of Ising models.
• Gauge invariance in the strong coupling BCS-model.
• On the algebraic properties of the Luttinger model.
• Dynamical groups and coexistence phenomena.