Isotropic N-point basis functions and their properties

被引:9
|
作者
Cahn, Robert N. [1 ]
Slepian, Zachary [1 ,2 ]
机构
[1] Lawrence Berkeley Natl Lab, Berkeley, CA 94720 USA
[2] Univ Florida, Dept Astron, Gainesville, FL 32611 USA
基金
美国国家航空航天局;
关键词
isotropic functions; expansion of isotropic functions; isotropy in cosmology; SPHERICAL HARMONIC-ANALYSIS; REDSHIFT DISTORTIONS; GAUSSIANITY; BISPECTRUM;
D O I
10.1088/1751-8121/acdfc4
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Isotropic functions of positions r(1), r(2),..., r(N), i.e. functions invariant under simultaneous rotations of all the coordinates, are conveniently formed using spherical harmonics and Clebsch-Gordan coefficients. An orthonormal basis of such functions provides a formalism suitable for analyzing isotropic distributions such as those that arise in cosmology, for instance in the clustering of galaxies as revealed by large-scale structure surveys. The algebraic properties of the basis functions are conveniently expressed in terms of 6-j and 9-j symbols. The calculation of relations among the basis functions is facilitated by 'Yutsis' diagrams for the addition and recoupling of angular momenta.
引用
收藏
页数:38
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