Symmetric Tensor Spherical Harmonics on the Sphere and Their Application to the De Sitter Group SO(,1)
Aug, 198654 pages
Published in:
- J.Math.Phys. 28 (1987) 1553,
- J.Math.Phys. 43 (2002) 6385 (erratum)
DOI:
Report number:
- YTP-86-19
Citations per year
Abstract: (AIP)
The symmetric tensor spherical harmonics (STSH’s) on the N‐sphere (S N ), which are defined as the totally symmetric, traceless, and divergence‐free tensor eigenfunctions of the Laplace–Beltrami (LB) operator on S N , are studied. Specifically, their construction is shown recursively starting from the lower‐dimensional ones. The symmetric traceless tensors induced by STSH’s are introduced. These play a crucial role in the recursive construction of STSH’s. The normalization factors for STSH’s are determined by using their transformation properties under SO(N+1). Then the symmetric, traceless, and divergence‐free tensor eigenfunctions of the LB operator in the N‐dimensional de Sitter space‐time which are obtained by the analytic continuation of the STSH’s on S N are studied. Specifically, the allowed eigenvalues of the LB operator under the restriction of unitarity are determined. Our analysis gives a group‐theoretical explanation of the forbidden mass range observed earlier for the spin‐2 field theory in de Sitter space‐time.- group: de Sitter
- GROUP THEORY: SO(N,1)
- GROUP THEORY: REPRESENTATION
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