Classical Particle in Presence of Magnetic Field, Hyperbolic Lobachevsky and Spherical Riemann Models
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 sol...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2010 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2010
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146095 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862639097152012288 |
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| author | Kudryashov, V.V. Kurochkin, Yu.A. Ovsiyuk, E.M. Red'kov, V.M. |
| author_facet | Kudryashov, V.V. Kurochkin, Yu.A. Ovsiyuk, E.M. Red'kov, V.M. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-01T00:29:19Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146095 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T00:29:19Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kudryashov, V.V. Kurochkin, Yu.A. Ovsiyuk, E.M. Red'kov, V.M. 2019-02-07T12:40:12Z 2019-02-07T12:40:12Z 2010 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. 1815-0659 2010 Mathematics Subject Classification: 37J35; 70G60; 70H06; 74H05 https://nasplib.isofts.kiev.ua/handle/123456789/146095 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Classical Particle in Presence of Magnetic Field, Hyperbolic Lobachevsky and Spherical Riemann Models Article published earlier |
| spellingShingle | Classical Particle in Presence of Magnetic Field, Hyperbolic Lobachevsky and Spherical Riemann Models Kudryashov, V.V. Kurochkin, Yu.A. Ovsiyuk, E.M. Red'kov, V.M. |
| title | Classical Particle in Presence of Magnetic Field, Hyperbolic Lobachevsky and Spherical Riemann Models |
| title_full | Classical Particle in Presence of Magnetic Field, Hyperbolic Lobachevsky and Spherical Riemann Models |
| title_fullStr | Classical Particle in Presence of Magnetic Field, Hyperbolic Lobachevsky and Spherical Riemann Models |
| title_full_unstemmed | Classical Particle in Presence of Magnetic Field, Hyperbolic Lobachevsky and Spherical Riemann Models |
| title_short | Classical Particle in Presence of Magnetic Field, Hyperbolic Lobachevsky and Spherical Riemann Models |
| title_sort | classical particle in presence of magnetic field, hyperbolic lobachevsky and spherical riemann models |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146095 |
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