Group Theoretical Methods in Physics

Inhaltsverzeichnis

• Group theory of the Morse potential.
• Four Euclidean conformal group approach to the multiphoton processes in the H-atom.
• Landau theory, symmetry breaking and the chain criterion.
• The configuration dN in cubic symmetry: A symmetry adapted weak field approach.
• Group theory of the effective potential.
• Bloch theorem for crystals with structural distortions.
• Global symmetries of spin systems defined on abelian manifolds.
• Phases and conjugacy classes.
• The probability density in non relativistic quantum mechanics and the (extended) Galilei group.
• Quaternionic quantum mechanics and Adler's chromostatics.
• Coherent angular momentum states for the isotropic oscillator.
• How to measure the canonical momentum p and operators p + f(q).
• A uniqueness result for the segal quantization of a classical system with symmetries.
• On the singular points of the matrix elements of the resolvent operator.
• Limitations on quantum measuring processes.
• Classical and quantum physics on phase space: The state spaces.
• Quantum dynamical semigroups and complete positivity. An application to isotropic spin relaxation.
• On geometric quantization of the rigid body.
• A unified theory of simple dynamical systems.
• Geometry of the time-dependent variational principle in quantum mechanics.
• Variational characterization of Hamiltonian vectorfields as lie algebra of canonical diffeomorphisms.
• The lie theory of extended groups in classical mechanics — Is it of relevance to quantum mechanics?.
• On the structure of phase space.
• Quantization as mapping and as deformation.
• Metric and group structures from quantum physics.
• Spontaneous symmetry breaking and restricted superposition principle.
• Many-body quantum mechanics as symplectic dynamics.
• A nonlinear superposition principle for Riccatiequations of the conformal type.
• Bäcklund transformations, conservation laws and lie symmetries for the generalized nonlinear Schrödinger equation.
• Killing tensors and variable separation for Hamilton-Jacobi equations.
• Lie pseudogroups and gauge theory.
• Conformal invariance and symmetry breaking for the one-dimensional wave equation.
• The flavour sequence and superselection rules.
• The Zitterbewegung of the electron and its compact phase space.
• New experimental evidence for a new interpretation of flavor SU(3).
• Baryon magnetic moments in broken SU(6).
• The Racah-Wigner algebra and the masses of exotic hadrons.
• Simple construction of a relativistic wave equation with arbitrary mass and spin and belinfante's 1/S-conjecture.
• Poincaré group, symplectic group, and relativistic extended hadrons consisting of spin 1/2 quarks.
• An operator S matrix theory of the strongly interacting particles.
• Generalized Galilei invariant partial wave expansions of the scattering amplitude for collisions between two particles with arbitrary spin.
• Ternary algebras as the basis of a dynamical theory of subconstituents.
• Solitons as sections in non trivial bundles.
• Effects of heavy colored higgs scalars in grand unified theories.
• Categories of nonlinear group realizations: A possible explanation for the multiple states of charge.
• Classical solutions of non-linear ?-models and their quantum fluctuations.
• Higgs representations for SO(n) gauges theories.
• Multivortex configurations in the Abelian Higgs model.
• Quark confinement in field theories with discrete gauge symmetry Z(3).
• Proliferation of effective fields by spontaneous symmetry breakdown.
• Explicit solutions for the scalar coupled Yang-Mills system in Minkowski space.
• Dynamical supersymmetry SU(6/4) in nuclei.
• Grouptheory of the IBA and its applications.
• Bases for irreps of U(6) and three body problems.
• Intrinsic sphape of nuclei.
• Group theory and nuclear high spin phenomena.
• SU3 symmetry in resonating group calculations. Toward a microscopic theory of 12C + 12C molecular resonances.
• Collective motion, composite particle structure, and symplectic groups in nuclei.
• Group theory and confrontation of nuclear collective models.
• Matrix elements of generators of U(6) in a U(6)? U(3)? U(2) basis.
• Hartree-Fock one-body dynamics and U(n) co-adjoint orbits.
• Group-theoretical aspects of the many-body problem in nuclear theory.
• The continuing quest for exact solutions of Einstein's field eouations - - new goals for the eighties.
• All non-twisting N's with cosmological constant.
• Can quantum effects prevent spacetime collapse?.
• Complex plane representation of the Geroch group and a proof of a geroch conjecture.
• The Geroch group and soliton solutions of the stationary axially symmetric Einstein's equations.
• Geometry of projective asymptotic twistor space.
• A truly relativistic approach of the concept of time.
• Bases in Sp(2n) representation space.
• Semiunitary projective representations of non-connected lie groups: A criterion for the choice of the unitary subgroup.
• SU(mn) ? SU(m) x SU(n) isoscalar factors and S(f1+f2) ? S(f1) × S(f2) isoscalar factors.
• Structure of enveloping algebras of low-rank groups.
• Computer programs for the reduction of symmetrised nth powers of space group irreducible representations using gard's subgroup method.
• Some remarks on the uniqueness and reality of Clebsch-Gordan coefficients for corepresentations.
• On some special relations involving 3-jm symbols.
• Two problems related to the Stone-von Neumann-Mackey uniqueness theorem.
• Non-complexrepresentations and their relation to antiunitary symmetry.
• Representation theory of compact groups.
• Representation theory of compact groups / Shift operators for discrete unitary representations of O(p, q).
• Representation theory of compact groups / Maximal Abelian subalgebras of sp(2n,?) and their applications in physics.
• Representation theory of compact groups / Polynomial space group tensors.
• A permutation for SUn consistent with duality.
• Integral transform representation of SL (2, R).
• The theory of G? supermanifolds.
• Casimir operations and the relations of the simplest supersymmetric superalgebra.
• On realizations of graded lie algebras and on properties of d-polynomials.
• On gauge formulations of gravitation theories.
• Lagrangian formalism for superfields with internal symmetry.
• Causal propagation in second order Lorentz-invariant wave equations.
• The exceptional group E8 for grand unification.
• Completely integrable N-body problems in three-dimension and their relativistic generalization.
• Ward-Takashi identities as a necessary and sufficient condition for gauce invariance.
• Supersymmetric generalization of Riemannian symmetric pairs.
• Composite gauge fields and Riemannian geometry.
• Gauge-theory ghosts and unitarity - Progress in the geometrical treatment.
• Color in internal supersymmetry unification.
• Canonical (possibly Lagrangian) realizations of the Poincare' group with increasing mass-spin trajectories.
• Similarity analysis of wave propagation in axially nonlinear nonhomogéneous systems.