Note on an improved classical limit of Clebsch-Gordan coefficients

TL;DR

This paper explores an improved classical limit of Clebsch-Gordan coefficients by analyzing a symmetrising shift related to permutation symmetry, extending Edmonds' classical limit with graphical illustrations.

Contribution

It introduces a novel extension of Edmonds' classical limit for Clebsch-Gordan coefficients using a symmetrising shift linked to permutation symmetry of 3-j symbols.

Findings

Extended Edmonds classical limit demonstrated

Graphical representations provided

Relation to permutation symmetry established

Abstract

A symmetrising shift employed by Frenkel and Hartnoll in the approximate computation of the elements of matrix spherical harmonics is further explored and shown to be related to the permutation symmetry of 3-j symbols yielding an extension of the Edmonds classical limit. Some graphs are displayed.