A new state sum model for 4D Lorentzian quantum gravity is constructed from quantum edge vectors and related to the Barrett-Crane spin foam model.
Spin foam model for Lorentzian General Relativity
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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.
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A state sum for four-dimensional Lorentzian quantum geometry in terms of edge vectors
A new state sum model for 4D Lorentzian quantum gravity is constructed from quantum edge vectors and related to the Barrett-Crane spin foam model.