Phys. Rev. D 63, 024022 (2000) [13 pages]Gluing 4-simplices: A derivation of the Barrett-Crane spin foam model for Euclidean quantum gravityReceived 10 October 2000; published 29 December 2000 We derive 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. © 2000 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevD.63.024022
DOI:
10.1103/PhysRevD.63.024022
PACS:
04.60.Gw, 04.60.Nc
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