Spin foam model for Lorentzian General Relativity

TL;DR

This paper introduces a spin foam model for Lorentzian quantum General Relativity, extending Euclidean models to incorporate Lorentzian signatures, and successfully reproduces key features like the Barrett-Crane vertex amplitude.

Contribution

It generalizes Euclidean spin foam models to Lorentzian signature, providing a consistent quantum gravity framework with the Barrett-Crane vertex.

Findings

The model reproduces the Barrett-Crane vertex amplitude.

It implements a sum over 2-complexes capturing local degrees of freedom.

The formulation extends spin foam models to Lorentzian spacetime.

Abstract

We present a spin foam formulation of Lorentzian quantum General Relativity. The theory is based on a simple generalization of an Euclidean model defined in terms of a field theory over a group. Its vertex amplitude turns out to be the one recently introduced by Barrett and Crane. As in the case of its Euclidean relatives, the model fully implements the desired sum over 2-complexes which encodes the local degrees of freedom of the theory.