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