Quaternionic Gauge Fields on S7 and Yang's SU(2) Monopole
Open Access
- 1 January 1980
- journal article
- Published by Oxford University Press (OUP) in Progress of Theoretical Physics
- Vol. 63 (1) , 303-321
- https://doi.org/10.1143/ptp.63.303
Abstract
A regular connection 1-form is introduced on a 7-sphere, and gauge transformations are applied to it to produce two specific singular connections. The gauge potentials which these singular connections embody are shown to be identical with Yang's SU(2) monopole solutions as shown by pulling back the latter by a Hopf map η2:S7→S4. The study is a genuine generalization of a previous work where Dirac's U(1) monopole was discussed within the realm of the Hopf fibre-map S3→S2: The present discussion hence parallels the previous one; a major difference being only that the quaternions are used in place of the complex numbers.Keywords
This publication has 1 reference indexed in Scilit:
- Solutions of the Maxwell and Yang-Mills equations associated with hopf fibringsInternational Journal of Theoretical Physics, 1977