### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 581-621 |

Number of pages | 41 |

Journal | Nuclear Physics B |

Volume | 796 |

Issue number | 3 |

DOIs | |

State | Published - Jun 21 2008 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*796*(3), 581-621. https://doi.org/10.1016/j.nuclphysb.2007.12.011

}

*Nuclear Physics B*, vol. 796, no. 3, pp. 581-621. https://doi.org/10.1016/j.nuclphysb.2007.12.011

**The perturbative Regge-calculus regime of loop quantum gravity.** / Bianchi, Eugenio; Modesto, Leonardo.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The perturbative Regge-calculus regime of loop quantum gravity

AU - Bianchi, Eugenio

AU - Modesto, Leonardo

PY - 2008/6/21

Y1 - 2008/6/21

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=40849083516&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=40849083516&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2007.12.011

DO - 10.1016/j.nuclphysb.2007.12.011

M3 - Article

AN - SCOPUS:40849083516

VL - 796

SP - 581

EP - 621

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -