Gluing 4-simplices: a derivation of the Barrett-Crane spin foam model for Euclidean quantum gravity

Abstract

We derive the the Barrett-Crane spin foam model for Euclidean 4 dimensional quantum gravity from a discretized BF theory, imposing the constraints that reduce it to gravity at the quantum level. We obtain in this way a precise prescription of the form of the Barrett-Crane state sum, in the general case of an arbitrary manifold with boundary. In particular we derive the amplitude for the edges of the spin foam from a natural procedure of gluing different 4-simplices along a common tetrahedron. The generalization of our results to higher dimensions is also shown.

26 pages, 7 figures; revised version: minor changes; to appear on Phys. Rev. D

References in corpus (3)

• A Lorentzian Signature Model for Quantum General Relativity
• Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space
• 4-dimensional BF Gravity on the Lattice

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