Eigenvalues and degeneracies for n‐dimensional tensor spherical harmonics

Symmetric transverse traceless tensor harmonics of arbitrary rank are constructed on spheres S n of dimensionality n≥3, and the associated eigenvalues of the Laplacian are computed. It is shown that these tensor harmonics span the space of symmetric transverse traceless tensors on S n and are eigenf...

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Bibliographic Details
Published in:Journal of mathematical physics 1984-10, Vol.25 (10), p.2888-2894
Main Authors: Rubin, Mark A., Ordóñez, Carlos R.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Function theory, analysis
Mathematical methods in physics
Physics
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Summary:Symmetric transverse traceless tensor harmonics of arbitrary rank are constructed on spheres S n of dimensionality n≥3, and the associated eigenvalues of the Laplacian are computed. It is shown that these tensor harmonics span the space of symmetric transverse traceless tensors on S n and are eigenfunctions of the quadratic Casimir operator of the group O(n+1). The dimensionalities of the eigenspaces of the Laplacian are computed for harmonics of rank 1 and rank 2.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.526034