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- Spin-weighted_spherical_harmonics abstract "In special functions, a topic in mathematics, 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 ℓ, 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 , and are typically denoted by , where ℓ 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. The spin-weighted spherical harmonics can be obtained from the standard spherical harmonics by application of spin raising and lowering operators. In particular, the spin-weighted spherical harmonics of spin weight s = 0 are simply the standard spherical harmonics:Spaces of spin-weighted spherical harmonics were first identified in connection with the representation theory of the Lorentz group (Gelfand, Minlos & Shapiro 1958). They were subsequently and independently rediscovered by Newman & Penrose (1966) and applied to describe gravitational radiation, and again by Wu & Yang (1976) as so-called "monopole harmonics" in the study of Dirac monopoles.".
- Spin-weighted_spherical_harmonics wikiPageExternalLink 1.
- Spin-weighted_spherical_harmonics wikiPageExternalLink 1.
- Spin-weighted_spherical_harmonics wikiPageExternalLink 1.
- Spin-weighted_spherical_harmonics wikiPageExternalLink Condon-ShortleyPhase.html.
- Spin-weighted_spherical_harmonics wikiPageExternalLink SpinWeightedSphericalHarmonics.nb.
- Spin-weighted_spherical_harmonics wikiPageID "6334535".
- Spin-weighted_spherical_harmonics wikiPageRevisionID "593082824".
- Spin-weighted_spherical_harmonics hasPhotoCollection Spin-weighted_spherical_harmonics.
- Spin-weighted_spherical_harmonics subject Category:Fourier_analysis.
- Spin-weighted_spherical_harmonics subject Category:Rotational_symmetry.
- Spin-weighted_spherical_harmonics subject Category:Special_functions.
- Spin-weighted_spherical_harmonics type Abstraction100002137.
- Spin-weighted_spherical_harmonics type Function113783816.
- Spin-weighted_spherical_harmonics type MathematicalRelation113783581.
- Spin-weighted_spherical_harmonics type Relation100031921.
- Spin-weighted_spherical_harmonics type SpecialFunctions.
- Spin-weighted_spherical_harmonics comment "In special functions, a topic in mathematics, 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.".
- Spin-weighted_spherical_harmonics label "Spin-weighted spherical harmonics".
- Spin-weighted_spherical_harmonics sameAs m.0g1kcy.
- Spin-weighted_spherical_harmonics sameAs Q7577353.
- Spin-weighted_spherical_harmonics sameAs Q7577353.
- Spin-weighted_spherical_harmonics sameAs Spin-weighted_spherical_harmonics.
- Spin-weighted_spherical_harmonics wasDerivedFrom Spin-weighted_spherical_harmonics?oldid=593082824.
- Spin-weighted_spherical_harmonics isPrimaryTopicOf Spin-weighted_spherical_harmonics.