The perturbative Regge-calculus regime of loop quantum gravity. (English) Zbl 1219.83077
Summary: The relation between loop quantum gravity and Regge calculus has been pointed out many times in the literature. In particular the large spin asymptotics of the Barrett-Crane vertex amplitude is known to be related to the Regge action. In this paper we study a semiclassical regime of loop quantum gravity and show that it admits an effective description in terms of perturbative area-Regge-calculus. The regime of interest is identified by a class of states given by superpositions of four-valent spin networks, peaked on large spins. As a probe of the dynamics in this regime, we compute explicitly two- and three-area correlation functions at the vertex amplitude level. We find that they match with the ones computed perturbatively in area-Regge-calculus with a single 4-simplex, once a specific perturbative action and measure have been chosen in the Regge-calculus path integral. Correlations of other geometric operators and the existence of this regime for other models for the dynamics are briefly discussed.
MSC:
| 83C45 | Quantization of the gravitational field |
| 81V17 | Gravitational interaction in quantum theory |
| 83C27 | Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory |
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