Asymptotics of LQG fusion coefficients

TL;DR

This paper derives an analytic formula for EPRL fusion coefficients in Loop Quantum Gravity, analyzes their large spin asymptotics, and demonstrates their role in connecting semiclassical intertwiners between SO(3) and SU(2)_L×SU(2)_R.

Contribution

It provides a simple analytic expression for fusion coefficients and studies their asymptotic behavior, revealing their role in semiclassical mapping in spin foam models.

Findings

Derived an explicit formula for EPRL fusion coefficients.

Showed asymptotic mapping of SO(3) to SU(2)_L×SU(2)_R intertwiners.

Highlighted implications for semiclassical analysis in Loop Quantum Gravity.

Abstract

The fusion coefficients from SO(3) to SO(4) play a key role in the definition of spin foam models for the dynamics in Loop Quantum Gravity. In this paper we give a simple analytic formula of the EPRL fusion coefficients. We study the large spin asymptotics and show that they map SO(3) semiclassical intertwiners into $SU(2)_L\times SU(2)_R$ semiclassical intertwiners. This non-trivial property opens the possibility for an analysis of the semiclassical behavior of the model.