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arXiv · 1403.0480

Geometry of the Hopf Bundle and spin-weighted Harmonics

Norbert Straumann
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Abstract

We demonstrate that it is conceptually and computationally favorable to regard spin-weighted spherical harmonics as vector valued functions on the total space $SO(3)$ of the Hopf bundle, satisfying a covariance condition with respect to the gauge group $U(1)$ of this bundle. A key role is played by the invariant connection form of the principle Hopf bundle, known to physicists from the geometry behind magnetic monopoles.

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Norbert Straumann. 2014-03-03. Geometry of the Hopf Bundle and spin-weighted Harmonics. https://arxiv.org/abs/1403.0480

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