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Geometry of the Hopf Bundle and spin-weighted Harmonics (1403.0480v1)
Published 3 Mar 2014 in gr-qc and math.DG
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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