Journal of Non-linear Mathematical Physics

ISSN: 1402-9251
Volume 11, Issue Supplement 1, October 2004

Geometrical Methods in Physics: Bialowieza XXI and XXII. Proceedings of the XXI and XXII Workshops on Geometrical Methods in Physics

June/July 2002 and 2003 Bialowieza, Poland

The round table of Bialowieza forest
Gérard G EMCH
Pages: 1 - 8
An overview of the lectures at the 2002 Bialowiea Workshop is presented. The symbol* after a proper name indicates that a copy of the corresponding contribution to the proceedings was communicated to the author of this summary.
Miloslav HAVLICEK, Jiri PATERA, Edita PELANTOVA, Jiri TOLAR
Pages: 37 - 42
We consider a special fine grading of sl(3, C), where the grading subspaces are geerated by 3 × 3 generalized Pauli matrices. This fine grading decomposes sl(3, C) into eight one­dimensional subspaces. Our aim is to find all contractions of sl(3, C) which preserve this grading. We have found that the...
Yuri VOROBIEV
Pages: 43 - 48
We show that every transitive Lie algebroid over a connected symplectic manifold comes from an intrinsic Lie algebroid of a symplectic leaf of a certain Poisson structure. The reconstruction of the corresponding Poisson structures from the Lie algebroid is given in terms of coupling tensors.
Martin SCHLICHENMAIER
Pages: 49 - 54
On an arbitrary almost-Kähler manifold, starting from a natural affine connection with nontrivial torsion which respects the almost-Kähler structure, in joint work with A. Karabegov a Fedosov-type deformation quantization on this manifold was costructed. This contribution reports on the result and...
Gilbert HONNOUVO, Mahouton Norbert HOUNKONNOU, Gabriel Yves Hugues
Pages: 66 - 71
Using the theory of self-adjoint extensions, we study the interaction model formally given by the Hamiltonian H + V (r), where H is the Aharonov-Bohm Hamiltonian and V (r) is the -type interaction potential on the cylinder of radius R . We give the mathematical definition of the model, the self-adjointness...
Vasyl KOVALCHUK
Pages: 72 - 77
The Green function for Klein-Gordon-Dirac equation is obtained. The case with the dominating Klein-Gordon term is considered. There seems to be a formal analogy between our problem and a certain problem for a 4-dimensional particle moving in the external field. The explicit relations between the wave...
A F KRACKLAUER
Pages: 104 - 109
A photoelectron-by-photoelectron classical simulation of EPR-B correlations is dscribed. It is shown that this model can be made compatible with Bell's renowned "no-go" theorem by restricting the source to that which produces only what is known as paired photons.
Alexander SHERMENEV
Pages: 110 - 115
Some classical types of nonlinear periodic wave motion are studied in special coodinates. In the case of cylinder coordinates, the usual perturbation techniques leads to the overdetermined systems of linear algebraic equations for unknown coefficients whose compatibility is key step of the investigation....
V.I. SERDOBOLSKII
Pages: 116 - 121
Solutions to basic non-linear limit spectral equation for matrices RT R of increasing dmension are investigated, where R are rectangular random matrices with independent normal entries. The analytical properties of limiting normed trace for the resolvent of RT R are investigated, boundaries of limit...
Galina GOUJVINA
Pages: 122 - 129
On a symplectical manifold M4 consider a Hamiltonian system with two degrees of freedom, integrable with the help of an additional integral f. According to the welknown Liouville theorem, non-singular level surfaces of the integrals H and f can be represented as unions of tori, cylinders and planes....
Agnieszka MARTENS
Pages: 145 - 150
This paper is a continuation of [1] where the classical model was analyzed. Discussed are some quantization problems of two-dimensional affinely rigid body with the double dynamical isotropy. Considered are highly symmetric models for which the variables can be separated. Some explicit solutions are...
Jan J. SLAWIANOWSKI, Vasyl KOVALCHUK
Pages: 157 - 166
The classical and quantum mechanics of systems on Lie groups and their homogeneous spaces are described. The special stress is laid on the dynamics of deformable bodies and the mutual coupling between rotations and deformations. Deformative modes are discretized, i.e., it is assumed that the relevant...
G. CHADZITASKOS, J. TOLAR
Pages: 174 - 178
We construct a deformation quantization for two cases of configuration spaces: the multiplicative group of positive real numbers R+ and the circle S1 . In these cases we define the momenta using the Fourier transform. Using the identification of symbols of quantum observables -- real functions on...
Sang-Ok HAHN, Phillial OH, Cheonsoo PARK, Sunyoung SHIN
Pages: 185 - 190
We study the Hamiltonian structure of the gauge symmetry breaking and enhancment. After giving a general discussion of these phenomena in terms of the constrained phase space, we perform a canonical analysis of the Grassmannian nonlinear sigma model coupled with Chern-Simons term, which contains a...
Dmitri VASSILIEV
Pages: 204 - 216
We consider spacetime to be a connected real 4-manifold equipped with a Lorentzian metric and an affine connection. The 10 independent components of the (symmetric) metric tensor and the 64 connection coefficients are the unknowns of our theory. We introduce an action which is quadratic in curvature...
Bogdan MIELNIK
Pages: 228 - 236
Data from many sources indicate that the Earth ecological crisis might not wait till distant future. To avert it, some difficult truth must be accepted and adequate steps taken. One of them is the strict protection of the world forests, even at the cost of the short term economic growth.