The 6j-symbol: Recursion, Correlations and Asymptotics

TL;DR

This paper analyzes the asymptotic behavior of the 6j-symbol using recursion relations, providing explicit higher-order corrections and applying these results to derive identities in 3D quantum gravity models.

Contribution

It introduces explicit formulas for higher-order asymptotic corrections of the 6j-symbol and connects recursion relations to quantum gravity correlation identities.

Findings

Explicit formulas for third-order corrections to the 6j-symbol asymptotics.

Derivation of Ward-Takahashi-like identities in 3D quantum gravity.

Application of recursion relations to spinfoam model correlations.

Abstract

We study the asymptotic expansion of the 6j-symbol using the Schulten-Gordon recursion relations. We focus on the particular case of the isosceles tetrahedron and we provide explicit formulas for up to the third order corrections beyond the leading order. Moreover, in the framework of spinfoam models for 3d quantum gravity, we show how these recursion relations can be used to derive Ward-Takahashi-like identities between the expectation values of graviton-like spinfoam correlations.