Finiteness of a spinfoam model for euclidean quantum general relativity

TL;DR

This paper proves that a specific spinfoam model for Euclidean quantum gravity, based on a field theory over multiple SO(4) groups, is finite with all Feynman diagrams converging, indicating mathematical consistency.

Contribution

It demonstrates the finiteness of a variant of the Barrett-Crane spinfoam model for Euclidean quantum gravity, a significant step in quantum gravity research.

Findings

All Feynman diagrams in the model converge.

The model is a finite, well-defined quantum gravity candidate.

It extends the Barrett-Crane model with proven mathematical consistency.

Abstract

We prove that a certain spinfoam model for euclidean quantum general relativity, recently defined, is finite: all its all Feynman diagrams converge. The model is a variant of the Barrett-Crane model, and is defined in terms of a field theory over SO(4) X SO(4) X SO(4) X SO(4).