Euclidean three-point function in loop and perturbative gravity

TL;DR

This paper compares the leading order three-point functions in loop quantum gravity and perturbative quantum general relativity, finding consistency in certain limits and exploring potential direct comparisons.

Contribution

It provides the first leading order computation of the three-point function in loop quantum gravity using spin foam dynamics and compares it with perturbative results.

Findings

Results are consistent with Regge calculus as gamma approaches zero.

Computed the tree-level three-point function in perturbative quantum gravity.

Discussed the potential for direct comparison between non-perturbative and perturbative approaches.

Abstract

We compute the leading order of the three-point function in loop quantum gravity, using the vertex expansion of the Euclidean version of the new spin foam dynamics, in the region of gamma<1. We find results consistent with Regge calculus in the limit gamma->0 and j->infinity. We also compute the tree-level three-point function of perturbative quantum general relativity in position space, and discuss the possibility of directly comparing the two results.