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 H3;
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 H3 and SO(3,1) homogeneity of the model;
7. Particle in magnetic field, spherical Riemann model S3;
8. Simplest solutions in spherical space;
9. Conserved quantity energy in Riemann space S3;
10. Particle in magnetic field and Lagrange formalism in spherical model S3;
11. All possible trajectories and SO(4) homogeneity of the space S3;
12. Space shifts and gauge symmetry of the uniform magnetic field in H3;
13. Space shifts in space S3 and gauge symmetry in magnetic field;
14. Particle in H3, special motions with constant angular velocity;
15. Particle in S3, special motions with constant angular velocity;
16. Hamilton-Jacobi approach on the background of hyperbolic geometry;
17. Hamilton-Jacobi approach on the background of spherical geometry;
18. On quantum mechanical problem in magnetic field, Schrödinger equation in H3 model;
19. On quantum mechanical problem in magnetic field, Schrödinger equation in S3 model;
20. Discussion: classification, finite and infinite motions.

This is joint work with V.V. Kudriashov, Yu.A. Kurochkin, E.M. Ovsiyuk.

Presentation