Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-07-19
Nucl.Phys. B574 (2000) 785-806
Physics
High Energy Physics
High Energy Physics - Theory
16 Pages (RevTeX), 4 eps figures. Minor revisions in the definition of the model
Scientific paper
10.1016/S0550-3213(00)00005-5
Boulatov and Ooguri have generalized the matrix models of 2d quantum gravity to 3d and 4d, in the form of field theories over group manifolds. We show that the Barrett-Crane quantum gravity model arises naturally from a theory of this type, but restricted to the homogeneous space S^3=SO(4)/SO(3), as a term in its Feynman expansion. From such a perspective, 4d quantum spacetime emerges as a Feynman graph, in the manner of the 2d matrix models. This formalism provides a precise meaning to the ``sum over triangulations'', which is presumably necessary for a physical interpretation of a spin foam model as a theory of gravity. In addition, this formalism leads us to introduce a natural alternative model, which might have relevance for quantum gravity.
Freidel Laurent
Krasnov Kirill
Pietri Roberto de
Rovelli Carlo
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