3+1 spinfoam model of quantum gravity with spacelike and timelike components

TL;DR

This paper introduces a Lorentzian spinfoam model of quantum gravity that incorporates both spacelike and timelike components, providing a non-perturbative framework with a natural causal structure based on the internal gauge algebra.

Contribution

It extends previous Lorentzian spinfoam models by including spacelike and timelike components within a unified quantum gravity formulation.

Findings

Model encodes a natural non-perturbative local causal structure.

Amplitudes are expressed as integrals over hyperboloids in Minkowski space.

Framework generalizes Euclidean models to Lorentzian signature with causal features.

Abstract

We present a spinfoam 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. The model is an extension of a recently introduced Lorentzian model, in which both timelike and spacelike components are included. The spinfoams in the model, corresponding to quantized 4-geometries, carry a natural non-perturbative local causal structure induced by the geometry of the algebra of the internal gauge (sl(2,C)). Amplitudes can be expressed as integrals over the spacelike unit-vectors hyperboloid in Minkowski space, or the imaginary Lobachevskian space.