Spherical-harmonic tensors
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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2020-10-01
|
| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.043061 |
| Summary: | 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. |
|---|---|
| ISSN: | 2643-1564 |