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 and small Barbero-Immirzi parameter 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: and . The models in the two spin regimes have dramatically different numbers of effective degrees of freedom. In , 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, , only a small deficit angle is allowed, . When spins become even larger, only a zero deficit angle 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.
- Received 10 May 2013
DOI:https://doi.org/10.1103/PhysRevD.88.044051
© 2013 American Physical Society