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Toulon, France

Han M.,University of Toulon
Classical and Quantum Gravity | Year: 2014

We study the semiclassical behavior of Lorentzian Engle-Pereira-Rovelli- Livine (EPRL) spinfoam model, by taking into account the sum over spins in the large spin regime. We also employ the method of stationary phase analysis with parameters and the so-called, almost analytic machinery, in order to find the asymptotic behavior of the contributions from all possible large spin configurations in the spinfoam model. The spins contributing the sum are written as Jf = λjf, where λ is a large parameter resulting in an asymptotic expansion via stationary phase approximation. The analysis shows that at least for the simplicial Lorentzian geometries (as spinfoam critical configurations), they contribute the leading order approximation of spinfoam amplitude only when their deficit angles satisfy mod . Our analysis results in a curvature expansion of the semiclassical low energy effective action from the spinfoam model, where the UV modifications of Einstein gravity appear as subleading high-curvature corrections. © 2014 IOP Publishing Ltd. Source

Han M.,University of Toulon
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2014

A low-energy perturbation theory is developed from the nonperturbative framework of covariant loop quantum gravity (LQG) by employing the background-field method. The resulting perturbation theory is a two-parameter expansion in the semiclassical and low-energy regime. The two expansion parameters are the large spin and small curvature. The leading-order effective action coincides with the Regge action, which well approximates the Einstein-Hilbert action in the regime. The subleading corrections organized by the two expansion parameters give the modifications of the Regge action in the quantum and high-energy regime from LQG. The perturbation theory developed here shows for the first time that covariant LQG produces the high-curvature corrections to Einstein-Regge gravity. This result means that LQG is not a naive quantization of Einstein gravity; rather, it provides the UV modification. The result of the paper may be viewed as the first step toward understanding the UV completeness of LQG. © 2014 American Physical Society. Source

Alibert J.-J.,University of Toulon | Della Corte A.,University of Rome La Sapienza
Zeitschrift fur Angewandte Mathematik und Physik | Year: 2015

Since the works by Gabrio Piola, it has been debated the relevance of higher-gradient continuum models in mechanics. Some authors even questioned the logical consistency of higher-gradient theories, and the applicability of generalized continuum theories seems still open. The present paper considers a pantographic plate constituted by Euler beams suitably interconnected and proves that Piola’s heuristic homogenization method does produce an approximating continuum in which deformation energy depends only on second gradients of displacements. The Γ-convergence argument presented herein shows indeed that Piola’s conjecture can be rigorously proven in a Banach space whose norm is physically dictated by energetic considerations. © 2015, Springer Basel. Source

Han M.,University of Toulon
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2013

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: 1-1 -2 and λ≥γ -2. The models in the two spin regimes have dramatically different numbers of effective degrees of freedom. In 1-1-2, 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, λ≥γ-2, only a small deficit angle is allowed, |Θf|-1λ-1/2 mod 4πZ. When spins become even larger, only a zero deficit angle mod 4πZ 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. © 2013 American Physical Society. Source

Riello A.,Aix - Marseille University | Riello A.,University of Toulon
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2013

We calculate the most divergent contribution to the nondegenerate sector of the self-energy (or "melonic") graph in the context of the Lorentzian Engle-Pereira-Rovelli-Livine and Freidel-Krasnov spin foam model of quantum gravity. We find that such a contribution is logarithmically divergent in the cutoff over the SU(2) representation spins when one chooses the face amplitude guaranteeing the face-splitting invariance of the foam. We also find that the dependence on the boundary data is different from that of the bare propagator. This fact has its origin in the noncommutativity of the Engle-Pereira-Rovelli- Livine and Freidel-Krasnov Yγ map with the projector onto SL(2,C)-invariant states. In the course of the paper, we discuss in detail the approximations used during the calculations, their geometrical interpretation, and the physical consequences of our result. © 2013 American Physical Society. Source

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