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

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

2000-10-09

arxiv.org/abs/gr-qc/0010031v2

Phys.Rev. D63 (2001) 024022

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1103/PhysRevD.63.024022

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.

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