The complete LQG propagator: II. Asymptotic behavior of the vertex
Emanuele Alesci, Carlo Rovelli
TL;DR
This work addresses the problem that the Barrett-Crane spinfoam vertex fails to reproduce the full graviton propagator in a background-independent LQG setting. The authors construct a vertex amplitude $W$ with an intertwiner-phase dependent asymptotic form and pair it with a carefully chosen boundary state to recover the full tensorial structure of the linearized graviton propagator, projected on the normals to boundary tetrahedra, in the large-distance limit. They show that, despite the complexity of intertwiner noncommutativity, the propagator can be obtained from a Gaussian integral controlled by five independent parameters, which can be tuned to match the five independent components of the linearized theory. This demonstrates that background-independent spinfoam dynamics can reproduce low-energy graviton physics and provides guidance on how to select dynamical amplitudes, with implications for alternative vertices such as the EPR vertex and further numerical and analytical exploration.
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.