Curvature in spinfoams

TL;DR

This paper demonstrates that spinfoam quantum gravity amplitudes project onto curved classical geometries, indicating a path integral over Regge metrics that enforces discrete Einstein equations in the classical limit.

Contribution

It introduces a new interpretation of the semiclassical limit for spinfoam amplitudes on fixed 2-complexes, linking them to discrete Einstein equations.

Findings

Spinfoam amplitudes project onto curved classical geometries.

In the semiclassical limit, amplitudes resemble a path integral over Regge metrics.

Results support the emergence of classical Einstein geometry from quantum spinfoams.

Abstract

We consider spinfoam quantum gravity. We show in a simple case that the amplitude projects over a nontrivial (curved) classical geometry. This suggests that, at least for spinfoams without bubbles and for large values of the boundary spins, the amplitude takes the form of a path integral over Regge metrics, thus enforcing discrete Einstein equations in the classical limit. The result relies crucially on a new interpretation of the semiclassical limit for the amplitudes truncated to a fixed 2-complex.