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

Alejandro Perez·Carlo Rovelli
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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.

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Alejandro Perez, Carlo Rovelli. 2000-11-10. 3+1 spinfoam model of quantum gravity with spacelike and timelike components. https://doi.org/10.1103/physrevd.64.064002

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