论文标题
各向同性的N点基函数及其属性
Isotropic N-Point Basis Functions and Their Properties
论文作者
论文摘要
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.此类功能的正直基础提供了一种适合分析各向同性分布的形式主义，例如在宇宙学中出现的分布，例如在星系的聚类中，如大规模结构调查所揭示的那样。基本功能的代数属性以6- $ j $和9- $ j $符号方便表示。基础函数之间关系的计算通过“ Yutsis”图促进了角动量的添加和重耦。
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.
