Reciprocity of the Wigner derivative for spherical tetrahedra

TL;DR

This paper demonstrates that for spherical tetrahedra, the inverse Wigner derivative equals the Wigner derivative, linking geometric derivatives to quantum 6j symbol asymptotics, revealing a reciprocity property.

Contribution

It computes the inverse Wigner derivative for spherical tetrahedra and proves its equality to the Wigner derivative, establishing a new reciprocity relation.

Findings

Inverse Wigner derivative equals the Wigner derivative for spherical tetrahedra

The results are motivated by asymptotics of classical and quantum 6j symbols for SU(2)

Establishes a geometric reciprocity property in spherical tetrahedra

Abstract

The Wigner derivative is the partial derivative of dihedral angle with respect to opposite edge length in a tetrahedron, all other edge lengths remaining fixed. We compute the inverse Wigner derivative for spherical tetrahedra, namely the partial derivative of edge length with respect to opposite dihedral angle, all other dihedral angles remaining fixed. We show that the inverse Wigner derivative is actually equal to the Wigner derivative. These computations are motivated by the asymptotics of the classical and quantum 6j symbols for SU(2).