Group Integral Techniques for the Spinfoam Graviton Propagator

TL;DR

This paper introduces a new boundary state ansatz in the spinfoam formalism, enabling the graviton propagator to be expressed as an SU(2) integral, and demonstrates its consistency with low-energy physics.

Contribution

It proposes a novel boundary state ansatz that simplifies the graviton propagator calculation within the spinfoam framework.

Findings

Leading order behavior matches low-energy physics expectations

Degenerate spinfoam configurations are suppressed

Integral representation facilitates saddle point expansion

Abstract

We consider the proposal of gr-qc/0508124 for the extraction of the graviton propagator from the spinfoam formalism. We propose a new ansatz for the boundary state, using which we can write the propagator as an integral over SU(2). The perturbative expansion in the Planck length can be recast into the saddle point expansion of this integral. We compute the leading order and recover the behavior expected from low-energy physics. In particular, we prove that the degenerate spinfoam configurations are suppressed.