Survey of Hopf fibrations and rotation conventions in mathematics and physics
Abstract
Description
We present a unifying framework for understanding several different versions of the Hopf fibration, and use this framework to reconcile two methods of representing rotations of 3-space by unitary matrices--the mathematician's convention based on quaternion algebra, and the physicist's convention based on the Bloch sphere.
8 pages, revised 11 September 2008, new introduction, reference added, some notation change for consistency and clarity, expanded appendix
8 pages, revised 11 September 2008, new introduction, reference added, some notation change for consistency and clarity, expanded appendix