Survey of Hopf fibrations and rotation conventions in mathematics and physics

Details Survey of Hopf fibrations and rotation conventions in mathematics and physics Survey of Hopf fibrations and rotation conventions in mathematics and physics

2008-08-22

arxiv.org/abs/0808.3089v2

Physics

Mathematical Physics

8 pages, revised 11 September 2008, new introduction, reference added, some notation change for consistency and clarity, expan

Scientific paper

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.

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