{"paper":{"title":"Particle Motion in Monopoles and Geodesics on Cones","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Maxence Mayrand","submitted_at":"2014-07-30T01:37:22Z","abstract_excerpt":"The equations of motion of a charged particle in the field of Yang's $\\mathrm{SU}(2)$ monopole in 5-dimensional Euclidean space are derived by applying the Kaluza-Klein formalism to the principal bundle $\\mathbb{R}^8\\setminus\\{0\\}\\to\\mathbb{R}^5\\setminus\\{0\\}$ obtained by radially extending the Hopf fibration $S^7\\to S^4$, and solved by elementary methods. The main result is that for every particle trajectory $\\mathbf{r}:I\\to\\mathbb{R}^5\\setminus\\{0\\}$, there is a 4-dimensional cone with vertex at the origin on which $\\mathbf{r}$ is a geodesic. We give an explicit expression of the cone for an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7919","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}