论文标题
球形谐波张量
Spherical-harmonic tensors
论文作者
论文摘要
探索了球形谐波和对称张量之间的连接。对于每个球形谐波，构建了相应的无纹状体对称张量。然后将这些张量扩展到包括非零的轨迹，为任何等级的对称张量提供了正顺序的角度特征。球形谐波张量与自旋加权球形谐波之间的关系得出了。结果促进了大量张量值功能的球形谐波扩展。讨论了几个简单的说明性示例，并使用形式主义来得出牛顿重力违反洛伦兹不变性的领先影响。
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.
