
Symmetry in Nonlinear Mathematical Physics  2009
Viktor Red'kov (B.I. Stepanov Institute of Physics of NAS of Belarus, Minsk, Belarus)
Classical particle in presence of magnetic field,
hyperbolic Lobachevsky and Spherical Riemann models
Abstract:
1. Newton second law in Lobachevsky space;
2. Particle in the uniform magnetic field, hyperbolic model H_{3};
3. Simplest solutions in Lobachevsky model;
4. Conserved quantity energy in hyperbolic case;
5. Particle in magnetic field and Lagrange formalism in
Lobachevsky space;
6. All possible trajectories in H_{3} and SO(3,1) homogeneity of the model;
7. Particle in magnetic field, spherical Riemann model S_{3};
8. Simplest solutions in spherical space;
9. Conserved quantity energy in Riemann space S_{3};
10. Particle in magnetic field and Lagrange formalism in spherical model S_{3};
11. All possible trajectories and SO(4) homogeneity of the space S_{3};
12. Space shifts and gauge symmetry of the uniform magnetic field in H_{3};
13. Space shifts in space S_{3} and gauge symmetry in magnetic field;
14. Particle in H_{3}, special motions
with constant angular velocity;
15. Particle in S_{3}, special motions
with constant angular velocity;
16. HamiltonJacobi approach on the background of hyperbolic geometry;
17. HamiltonJacobi approach on the background of spherical geometry;
18. On quantum mechanical problem in magnetic field, Schrödinger equation in H_{3} model;
19. On quantum mechanical problem in magnetic field, Schrödinger equation in S_{3} model;
20. Discussion: classification, finite and infinite motions.
This is joint work with V.V. Kudriashov, Yu.A. Kurochkin, E.M. Ovsiyuk.
Presentation

