Spin-Weighted Spherical Harmonics (Paperback)

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.