Spin-s Spherical Harmonics and ð

1967/11/01 by Joshua N. Goldberg, Alan Macfarlane, Ezra T. Newman +2 · 16 citations
Mathematics · Earth and Planetary Sciences · #Algebraic and Geometric Analysis #Geophysics and Gravity Measurements #Mathematics and Applications #Spin-weighted spherical harmonics #Lorentz group #Spherical harmonics #Group (periodic table) #Tensor operator #Vector spherical harmonics #Lorentz transformation #Operator (biology) #Spin (aerodynamics) #Physics #Angular momentum #Mathematical physics #Conformal map #Mathematics #Rotation group SO #Harmonics #Rotation (mathematics) #Conformal group #Classical mechanics #Mathematical analysis #Quantum mechanics #Conformal symmetry #Geometry

paper · doi:10.1063/1.1705135

openalex publication_date 1967/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Recent work on the Bondi-Metzner-Sachs group introduced a class of functions sYlm(θ, φ) defined on the sphere and a related differential operator ð. In this paper the sYlm are related to the representation matrices of the rotation group R3 and the properties of ð are derived from its relationship to an angular-momentum raising operator. The relationship of the sTlm(θ, φ) to the spherical harmonics of R4 is also indicated. Finally using the relationship of the Lorentz group to the conformal group of the sphere, the behavior of the sTlm under this latter group is shown to realize a representation of the Lorentz group.

Citations

• Note on the Bondi-Metzner-Sachs Group
• The apparent shape of a relativistically moving sphere
• An Approach to Gravitational Radiation by a Method of Spin Coefficients
• Asymptotic Symmetries in Gravitational Theory

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