Semiclassical analysis of spinfoam model with a small Barbero-Immirzi parameter

Muxin Han
Phys. Rev. D 88, 044051 – Published 27 August 2013

Abstract

We study the semiclassical behavior of the Lorentzian Engle-Pereira-Rovelli-Livine spinfoam model by taking into account the sum over spins in the large spin regime. The large spin parameter λ and small Barbero-Immirzi parameter γ are treated as two independent parameters for the asymptotic expansion of the spinfoam state sum [such an idea was first pointed out in E. Magliaro and C. Perini, Europhys. Lett. 95, 30007 (2011); E. MagliaroC. PeriniInt. J. Mod. Phys. D 22, 1350001 (2013)]. Interestingly, there are two different spin regimes: 1γ1λγ2 and λγ2. The models in the two spin regimes have dramatically different numbers of effective degrees of freedom. In 1γ1λγ2, the model produces, in the leading order, a functional integration of the Regge action, which gives the discrete Einstein equation for the leading contribution. There is no restriction on the Lorentzian deficit angle in this regime. In the other regime, λγ2, only a small deficit angle is allowed, |Θf|γ1λ1/2mod4πZ. When spins become even larger, only a zero deficit angle mod4πZ is allowed asymptotically. In the transition of the two regimes, only the configurations with a small deficit angle can contribute, which means one needs a large triangulation in order to have oscillatory behavior of the spinfoam amplitude.

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  • Received 10 May 2013

DOI:https://doi.org/10.1103/PhysRevD.88.044051

© 2013 American Physical Society

Authors & Affiliations

Muxin Han*,†

  • Centre de Physique Théorique, CNRS UMR7332, Aix-Marseille Université and Université de Toulon, 13288 Marseille, France

  • *Muxin.Han@cpt.univ-mrs.fr
  • Unité mixte de recherche (UMR 6207) du CNRS et des Universités de Provence (Aix-Marseille I), de la Meditarranée (Aix-Marseille II) et du Sud (Toulon-Var); laboratoire affilié à la FRUMAM (FR 2291).

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Issue

Vol. 88, Iss. 4 — 15 August 2013

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