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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| Дата: | 2014 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146546 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Particle Motion in Monopoles and Geodesics on Cones/ M. Mayrand // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 35 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1465462019-02-10T01:25:03Z Particle Motion in Monopoles and Geodesics on Cones Mayrand, M. 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. 2014 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146546 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Mayrand, M. |
| spellingShingle |
Mayrand, M. Particle Motion in Monopoles and Geodesics on Cones Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Mayrand, M. |
| author_sort |
Mayrand, M. |
| title |
Particle Motion in Monopoles and Geodesics on Cones |
| title_short |
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_sort |
particle motion in monopoles and geodesics on cones |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146546 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT mayrandm particlemotioninmonopolesandgeodesicsoncones |
| first_indexed |
2025-07-11T00:13:12Z |
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2025-07-11T00:13:12Z |
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1837307314534612992 |