Tensor and Spinor Spherical Harmonics and the Spin‐s Harmonics sYlm(θ, φ)
Tensor and Spinor Spherical Harmonics and the Spin‐s Harmonics sYlm(θ, φ)
复制标题
张量和旋量球谐函数以及自旋 s 谐函数 sYlm(θ, φ)
DOI：
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发表时间：
1971
期刊：
影响因子：
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通讯作者：
W. B. Campbell
中科院分区：
文献类型：
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作者：
W. B. Campbell
由Newman和Penrose，SYlm(θ，φ)的自旋加权谐函数构造了一组笛卡尔张量球谐函数。结果表明，这些张量谐函数是总角动量、总角动量z分量、总自旋和自旋径向分量的本征函数。特别是，−S可能被认为是向外辐射的螺旋星。张量算符被引入，它降低和提高了螺旋度。它们被证明对应于由Newman和Penrose引入的算子In和In。由于SYLm(θ，φ)可以定义为L、m和S的半整数值，因此我们还构造了一组旋量球谐函数，它的性质与张量函数的性质相平行。
A set of Cartesian tensor spherical harmonics is constructed from the spin weighted harmonics of Newman and Penrose, sYlm(θ, φ). It is shown that these tensor harmonics are eigenfunctions of total angular momentum, z component of total angular momentum, total spin and radial component of spin. In particular, − s may be thought of as a helicity for outgoing radiation. Tensor operators are introduced which lower and raise this helicity. They are shown to correspond to the operators ð and ð introduced by Newman and Penrose. Because the sYlm(θ, φ) can be defined for half‐integer values of l, m, and s, a set of spinor spherical harmonics is also constructed which has properties paralleling those of the tensor harmonics.