球谐张量
Spherical-harmonic tensors
摘要：
球谐函数和对称张量之间的联系进行了探讨。对于每一个球谐函数，构造了相应的无迹对称张量。这些张量，然后扩展到包括非零的痕迹，提供一个正交的角动量特征基的对称张量的任何秩。球谐张量和自旋加权球谐张量之间的关系。这些结果有助于一大类张量值函数的球谐展开。几个简单的说明性的例子进行了讨论，和形式主义是用来推导的领导阶牛顿引力的违反洛伦兹不变性的影响。
英文摘要：
The connection between spherical harmonics and symmetric tensors is explored. For each spherical harmonic, a corresponding traceless symmetric tensor is constructed. These tensors are then extended to include nonzero traces, providing an orthonormal angular-momentum eigenbasis for symmetric tensors of any rank. The relationship between the spherical-harmonic tensors and spin-weighted spherical harmonics is derived. The results facilitate the spherical-harmonic expansion of a large class of tensor-valued functions. Several simple illustrative examples are discussed, and the formalism is used to derive the leading-order effects of violations of Lorentz invariance in Newtonian gravity.
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