The complete LQG propagator: II. Asymptotic behavior of the vertex

TL;DR

This paper demonstrates that a modified vertex amplitude in loop quantum gravity, which depends on intertwiners, can produce the correct graviton propagator asymptotically, addressing previous difficulties.

Contribution

It introduces a vertex amplitude dependent on intertwiners that successfully reproduces the graviton propagator in the large distance limit.

Findings

A specific asymptotic form of the vertex amplitude yields the correct propagator.

Dependence on intertwiners is crucial for obtaining the correct graviton propagator.

Addresses previous issues with Barrett-Crane vertex amplitude.

Abstract

In a previous article we have show that there are difficulties in obtaining the correct graviton propagator from the loop-quantum-gravity dynamics defined by the Barrett-Crane vertex amplitude. Here we show that a vertex amplitude that depends nontrivially on the intertwiners can yield the correct propagator. We give an explicit example of asymptotic behavior of a vertex amplitude that gives the correct full graviton propagator in the large distance limit.