Particle Motion in Monopoles and Geodesics on Cones
The equations of motion of a charged particle in the field of Yang's SU(2) monopole in 5-dimensional Euclidean space are derived by applying the Kaluza-Klein formalism to the principal bundle R⁸∖{0}→R⁵∖{0} obtained by radially extending the Hopf fibration S⁷→S⁴, and solved by elementary methods...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2014 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146546 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Particle Motion in Monopoles and Geodesics on Cones/ M. Mayrand // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 35 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862752203303813120 |
|---|---|
| author | Mayrand, M. |
| author_facet | Mayrand, M. |
| citation_txt | Particle Motion in Monopoles and Geodesics on Cones/ M. Mayrand // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 35 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The equations of motion of a charged particle in the field of Yang's SU(2) monopole in 5-dimensional Euclidean space are derived by applying the Kaluza-Klein formalism to the principal bundle R⁸∖{0}→R⁵∖{0} obtained by radially extending the Hopf fibration S⁷→S⁴, and solved by elementary methods. The main result is that for every particle trajectory r:I→R⁵∖{0}, there is a 4-dimensional cone with vertex at the origin on which r is a geodesic. We give an explicit expression of the cone for any initial conditions.
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| first_indexed | 2025-12-07T21:15:51Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146546 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:15:51Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Mayrand, M. 2019-02-09T21:13:10Z 2019-02-09T21:13:10Z 2014 Particle Motion in Monopoles and Geodesics on Cones/ M. Mayrand // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 35 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 70H06; 34A26; 53B50 DOI:10.3842/SIGMA.2014.102 https://nasplib.isofts.kiev.ua/handle/123456789/146546 The equations of motion of a charged particle in the field of Yang's SU(2) monopole in 5-dimensional Euclidean space are derived by applying the Kaluza-Klein formalism to the principal bundle R⁸∖{0}→R⁵∖{0} obtained by radially extending the Hopf fibration S⁷→S⁴, and solved by elementary methods. The main result is that for every particle trajectory r:I→R⁵∖{0}, there is a 4-dimensional cone with vertex at the origin on which r is a geodesic. We give an explicit expression of the cone for any initial conditions. The author is grateful to Professor Niky Kamran for his constant guidance and invaluable
 suggestions. The author would also like to thank the anonymous referees who provided helpful
 comments, corrections and reference suggestions. This work was supported by the NSERC
 USRA program, grant number RGPIN 105490-2011. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Particle Motion in Monopoles and Geodesics on Cones Article published earlier |
| spellingShingle | Particle Motion in Monopoles and Geodesics on Cones Mayrand, M. |
| title | Particle Motion in Monopoles and Geodesics on Cones |
| title_full | Particle Motion in Monopoles and Geodesics on Cones |
| title_fullStr | Particle Motion in Monopoles and Geodesics on Cones |
| title_full_unstemmed | Particle Motion in Monopoles and Geodesics on Cones |
| title_short | Particle Motion in Monopoles and Geodesics on Cones |
| title_sort | particle motion in monopoles and geodesics on cones |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146546 |
| work_keys_str_mv | AT mayrandm particlemotioninmonopolesandgeodesicsoncones |