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Spin-s Spherical Harmonics and ð

Journal of Mathematical Physics · 1967 · Vol. 8(11) · pp. 2155–2161

Joshua N. Goldberg✉(Syracuse University)Alan Macfarlane(Syracuse University)Ezra T. Newman(University of Pittsburgh)F. Rohrlich(Syracuse University)E. C. G. Sudarshan(Syracuse University)

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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.

Algebraic and Geometric Analysis Geophysics and Gravity Measurements Mathematics and ApplicationsSpin-weighted spherical harmonicsLorentz groupSpherical harmonicsGroup (periodic table)Tensor operatorVector spherical harmonicsLorentz transformationOperator (biology)Spin (aerodynamics)Physics

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