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Particle Motion in Monopoles and Geodesics on Cones
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Particle Motion in Monopoles and Geodesics on Cones
Інший ID:
2010 Mathematics Subject Classification: 70H06; 34A26; 53B50
DOI:10.3842/SIGMA.2014.102
DOI:10.3842/SIGMA.2014.102
Посилання:
Particle Motion in Monopoles and Geodesics on Cones/ M. Mayrand // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 35 назв. — англ.
Підтримка:
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.
Дата:
2014
Переглядів:
594
Завантажень:
269
Анотація:
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.
