Prog. Theor. Phys. Vol. 68 No. 1 (1982) pp. 310-313

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Letters

Tensor Spherical and Pseudo-Spherical Harmonics in Four-Dimensional Spaces

Kenji Tomita

Research Institute for Theoretical Physics, Hiroshima University, Takehara, Hiroshima 725

(Received February 22, 1982)

Abstract:

Explicit expressions for tensor spherical harmonics on the 3 sphere in the four-dimensional Euclidean space are derived, and extended to derive those for pseudo-spherical harmonics. They are useful for the analyses of large-scale perturbations in the Friedmann universe models.

URL : http://ptp.ipap.jp/link?PTP/68/310/
DOI : 10.1143/PTP.68.310

References:

S. P. Boughin, E. S. Cheng and D. T. Wilkinson, Astrophys. J. 243 (1981), L113 [CrossRef]
See also M. V. Gorenstein and G. F. Smoot, Astrophys. J. 244 (1981), 361[CrossRef].
E. M. Lifshitz, J. Phys. (USSR) 10 (1946), 116.
E. M. Lifshitz and I. M. Khalatnikov, Adv. Phys. 12 (1963), 185. See Appendix J.
T. Regge and J. A. Wheeler, Phys. Rev. 108 (1957), 1063[APS].
F. J. Zerilli, J. Math. Phys. 11 (1970), 2203[CrossRef].
M. Daumens and P. Minnaert, J. Math. Phys. 17 (1976), 1903[CrossRef]; ibid. 17 (1976), 2085[CrossRef].

Citing Article(s) :

Progress of Theoretical Physics Vol. 69 No. 3 (1983) pp. 828-841 :
Large-Scale Anisotropy of the Cosmic Background Radiation Due to Primordial Density and Gravitational-Wave Perturbations

Kenji Tomita and Kenji Tanabe
Progress of Theoretical Physics Vol. 97 No. 2 (1997) pp. 243-262 :
The Spectrum of Gravitational Wave Perturbations in the One-Bubble Open Inflationary Universe

Takahiro Tanaka and Misao Sasaki