Symmetric tensor spherical harmonics on the N-sphere and their application to the de Sitter group SO(N,1)

Journal Article · Wed Jul 01 04:00:00 EDT 1987 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.527513· OSTI ID:6597484

Higuchi, A

The symmetric tensor spherical harmonics (STSH's) on the N-sphere (S/sup N/), which are defined as the totally symmetric, traceless, and divergence-free tensor eigenfunctions of the Laplace--Beltrami (LB) operator on S/sup 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/sup 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.

• Research Organization: Physics Department, Yale University, New Haven, Connecticut 06511 and Department of Physics, University of Wisconsin--Milwaukee, Milwaukee, Wisconsin 53201
• OSTI ID: 6597484
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 28:7; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COSMOLOGY
DE SITTER GROUP
EINSTEIN FIELD EQUATIONS
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
GENERAL RELATIVITY THEORY
GROUP THEORY
LIE GROUPS
MATHEMATICAL OPERATORS
MATHEMATICS
QUANTUM OPERATORS
RECURSION RELATIONS
SO GROUPS
SPACE-TIME
SPHERICAL HARMONICS
SYMMETRY
SYMMETRY GROUPS
TENSORS