Abstract
We present a spin foam formulation of Lorentzian quantum general relativity. The theory is based on a simple generalization of a 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 spin foams in the model, corresponding to quantized 4-geometries, carry a natural nonperturbative local causal structure induced by the geometry of the algebra of the internal gauge Amplitudes can be expressed as integrals over the spacelike unit vectors hyperboloid in Minkowski space, or the imaginary Lobachevskian space.
- Received 25 January 2001
DOI:https://doi.org/10.1103/PhysRevD.64.064002
©2001 American Physical Society