A Discrete and Coherent Basis of Intertwiners

TL;DR

This paper introduces a new discrete, coherent basis for 4-valent SU(2) intertwiners, enabling accurate classical representation and asymptotic analysis of spin network amplitudes, including the first asymptotics of 15j symbols in the real basis.

Contribution

It constructs a novel discrete, coherent basis for 4-valent SU(2) intertwiners and derives their asymptotic behavior, including the first analysis of 15j symbols in the real basis.

Findings

New discrete basis for 4-valent SU(2) intertwiners

Generalized Racah formula for arbitrary graph amplitudes

Asymptotic analysis revealing a Regge-like action for twisted geometries

Abstract

We construct a new discrete basis of 4-valent SU(2) intertwiners. This basis possesses both the advantage of being discrete, while at the same time representing accurately the classical degrees of freedom; hence it is coherent. The closed spin network amplitude obtained from these intertwiners depends on twenty spins and can be evaluated by a generalization of the Racah formula for an arbitrary graph. The asymptotic limit of these amplitudes is found. We give, for the first time, the asymptotics of 15j symbols in the real basis. Remarkably it gives a generalization of the Regge action to twisted geometries.