Spin-weighted Spherical Harmonics
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High Quality Content by WIKIPEDIA articles! Spin-weighted spherical harmonics are generalizations of the standard spherical harmonics and like the usual spherical harmonics are functions on the sphere. Unlike ordinary spherical harmonics, the spin-weighted harmonics are U(1) gauge fields rather than scalar fields: mathematically, they take values in a complex line bundle. The spin-weighted harmonics are organized by degree , just like ordinary spherical harmonics, but have an additional spin weight s that reflects the additional U(1) symmetry. A special basis of harmonics can be derived from t...
High Quality Content by WIKIPEDIA articles! Spin-weighted spherical harmonics are generalizations of the standard spherical harmonics and like the usual spherical harmonics are functions on the sphere. Unlike ordinary spherical harmonics, the spin-weighted harmonics are U(1) gauge fields rather than scalar fields: mathematically, they take values in a complex line bundle. The spin-weighted harmonics are organized by degree , just like ordinary spherical harmonics, but have an additional spin weight s that reflects the additional U(1) symmetry. A special basis of harmonics can be derived from the Laplace spherical harmonics Y_{ell m}, and are typically denoted by {}_sY_{ell m}, where and m are the usual parameters familiar from the standard Laplace spherical harmonics. In this special basis, the spin-weighted spherical harmonics appear as actual functions, because the choice of a polar axis fixes the U(1) gauge ambiguity.
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