Semiclassical Limit of New Spin Foam Models

TL;DR

This paper analyzes the semiclassical limit of new spin foam models in Loop Quantum Gravity, showing that their graviton propagator behaves as the inverse fourth power of distance, consistent with classical gravity.

Contribution

It demonstrates that all new spin foam models share the same large-spin asymptotics leading to the correct graviton propagator behavior.

Findings

Graviton propagator scales as inverse fourth power of distance.

Large-spin asymptotics determine the propagator behavior.

Identifies vertex amplitude asymptotics yielding correct graviton propagator.

Abstract

We study the problem of semiclassical limit of Loop Quantum Gravity theory defined by the new spin foam models. This is done by analyzing the large-spin asymptotics of the Hartle-Hawking wavefunction. By using the stationary phase method we determine the wavefunction asymptotics, which then determines the large-distance asymptotics of the corresponding graviton propagator. We show that the graviton propagator behaves as the inverse distance to the fourth power. Our result is a direct consequence of the large-spin asymptotics of the spin foam model vertex amplitude, and it is valid for all new spin foam models, since they all have the same type of the vertex amplitude asymptotics. We also find the type of the vertex amplitude asymptotics which gives the correct graviton propagator.