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Classical Particle in Presence of Magnetic Field, Hyperbolic Lobachevsky and Spherical Riemann Models
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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Classical Particle in Presence of Magnetic Field, Hyperbolic Lobachevsky and Spherical Riemann Models
Інший ID:
2010 Mathematics Subject Classification: 37J35; 70G60; 70H06; 74H05
Посилання:
Classical Particle in Presence of Magnetic Field, Hyperbolic Lobachevsky and Spherical Riemann Models / V.V. Kudryashov, Yu.A. Kurochkin, E.M. Ovsiyuk, V.M. Red'kov // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 19 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the Eighth International Conference “Symmetry in Nonlinear Mathematical Physics” (June 21–27, 2009, Kyiv, Ukraine). The full collection is available at http://www.emis.de/journals/SIGMA/symmetry2009.html.
Authors are grateful to participants of seminar of Laboratory of Theoretical Physics, National Academy of Sciences of Belarus for moral support and advice, also we are grateful to anonymous reviewers for stimulating discussion and criticism. This work was also supported by the Fund for Basic Researches of Belarus F09K-123. We wish to thank the Organizers of the VIII-th International Conference “Symmetry in Nonlinear Mathematical Physics” (June 21–27, 2009, Kyiv) for having given us the opportunity to talk on this subject as well as for local support.
Дата:
2010
Переглядів:
516
Завантажень:
205
Анотація:
Motion of a classical particle in 3-dimensional Lobachevsky and Riemann spaces is studied in the presence of an external magnetic field which is analogous to a constant uniform magnetic field in Euclidean space. In both cases three integrals of motions are constructed and equations of motion are solved exactly in the special cylindrical coordinates on the base of the method of separation of variables. In Lobachevsky space there exist trajectories of two types, finite and infinite in radial variable, in Riemann space all motions are finite and periodical. The invariance of the uniform magnetic field in tensor description and gauge invariance of corresponding 4-potential description is demonstrated explicitly. The role of the symmetry is clarified in classification of all possible solutions, based on the geometric symmetry group, SO(3,1) and SO(4) respectively.
