Tensorial Structure of the LQG graviton propagator

TL;DR

This paper analyzes the tensorial structure of the graviton propagator within loop quantum gravity, highlighting limitations of the Barrett-Crane vertex and discussing an alternative vertex that produces correct long-distance behavior.

Contribution

It demonstrates that the Barrett-Crane vertex fails to produce the correct propagator due to intertwiner-independence, and reviews an alternative vertex with proper asymptotic behavior.

Findings

Barrett-Crane vertex cannot yield correct propagator in the long distance limit

Intertwiner-independence causes limitations in the Barrett-Crane model

An alternative vertex reproduces the correct asymptotic behavior

Abstract

We review the construction of the tensorial structure of the graviton propagator in the context of loop quantum gravity and spinfoam formalism. The main result of this analysis is that applying the same strategy used to compute the diagonal terms, the Barrett-Crane vertex is unable to yield the correct propagator in the long distance limit. The problem is in the intertwiner-independence of the Barrett-Crane vertex. We also review the asymptotic behavior of an alternative vertex that is able to give the correct propagator.