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 [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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