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

Daniele Oriti·Ruth M. Williams
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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.

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Daniele Oriti, Ruth M. Williams. 2000-12-04. Gluing 4-simplices: a derivation of the Barrett-Crane spin foam model for Euclidean quantum gravity. https://doi.org/10.1103/physrevd.63.024022

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