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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2020-10-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.043061 |
| _version_ | 1797211226395115520 |
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| author | Francisco Gonzalez Ledesma Matthew Mewes |
| author_facet | Francisco Gonzalez Ledesma Matthew Mewes |
| author_sort | Francisco Gonzalez Ledesma |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T10:23:07Z |
| format | Article |
| id | doaj.art-b3baef928c1b4709ba7082f4c58b9ad5 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:23:07Z |
| publishDate | 2020-10-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-b3baef928c1b4709ba7082f4c58b9ad52024-04-12T17:02:12ZengAmerican Physical SocietyPhysical Review Research2643-15642020-10-012404306110.1103/PhysRevResearch.2.043061Spherical-harmonic tensorsFrancisco Gonzalez LedesmaMatthew MewesThe 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.http://doi.org/10.1103/PhysRevResearch.2.043061 |
| spellingShingle | Francisco Gonzalez Ledesma Matthew Mewes Spherical-harmonic tensors Physical Review Research |
| title | Spherical-harmonic tensors |
| title_full | Spherical-harmonic tensors |
| title_fullStr | Spherical-harmonic tensors |
| title_full_unstemmed | Spherical-harmonic tensors |
| title_short | Spherical-harmonic tensors |
| title_sort | spherical harmonic tensors |
| url | http://doi.org/10.1103/PhysRevResearch.2.043061 |
| work_keys_str_mv | AT franciscogonzalezledesma sphericalharmonictensors AT matthewmewes sphericalharmonictensors |