Isotropic N-point basis functions and their properties - INSPIRE

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Isotropic N-point basis functions and their properties

Oct 27, 2020

57 pages

Published in:

J.Phys.A 56 (2023) 32, 325204

Published: Jul 21, 2023

e-Print:

2010.14418 [astro-ph.CO]

DOI:

10.1088/1751-8121/acdfc4

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Abstract: (IOP)

Isotropic functions of positions , 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.

Note:

57 pages, submitted to Journal of Mathematical Physics, comments welcome

isotropic functions
expansion of isotropic functions
isotropy in cosmology

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