Isotropic N-point basis functions and their properties
Abstract
Isotropic functions of positions $\textbf{r}_1,\textbf{r}_2, \ldots, \textbf{r}_N$ , 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.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- August 2023
- DOI:
- 10.1088/1751-8121/acdfc4
- arXiv:
- arXiv:2010.14418
- Bibcode:
- 2023JPhA...56F5204C
- Keywords:
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- isotropic functions;
- expansion of isotropic functions;
- isotropy in cosmology;
- Astrophysics - Cosmology and Nongalactic Astrophysics;
- Mathematical Physics
- E-Print:
- 57 pages, submitted to Journal of Mathematical Physics, comments welcome