Spherical-harmonic tensors
Classical Physics
2020-10-20 v1
Abstract
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.
Cite
@article{arxiv.2010.09433,
title = {Spherical-harmonic tensors},
author = {Francisco Gonzalez Ledesma and Matthew Mewes},
journal= {arXiv preprint arXiv:2010.09433},
year = {2020}
}
Comments
17 pages