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arXiv · 2010.14418

Isotropic N-Point Basis Functions and Their Properties

Robert N. Cahn·Zachary Slepian
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Abstract

Isotropic functions of positions $\hat{\bf r}_1, \hat{\bf r}_2,\ldots, \hat{\bf r}_N$, 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.

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Robert N. Cahn, Zachary Slepian. 2020-10-27. Isotropic N-Point Basis Functions and Their Properties. https://doi.org/10.1088/1751-8121%2Facdfc4

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