Physical boundary state for the quantum tetrahedron

We consider stability under evolution as a criterion to select a physical boundary state for the spinfoam formalism. As an example, we apply it to the simplest spinfoam defined by a single quantum tetrahedron and solve the associated eigenvalue problem at leading order in the large spin limit. We show that this fixes uniquely the free parameters entering the boundary state. Remarkably, the state obtained this way gives a correlation between edges which runs at leading order with the inverse distance between the edges, in agreement with the linearized continuum theory. Finally, we give an argument why this correlator represents the propagation of a pure gauge, consistently with the absence of physical degrees of freedom in 3d general relativity.Comment: 20 pages, 6 figure

Numerical indications on the semiclassical limit of the flipped vertex

We introduce a technique for testing the semiclassical limit of a quantum gravity vertex amplitude. The technique is based on the propagation of a semiclassical wave packet. We apply this technique to the newly introduced "flipped" vertex in loop quantum gravity, in order to test the intertwiner dependence of the vertex. Under some drastic simplifications, we find very preliminary, but surprisingly good numerical evidence for the correct classical limit.Comment: 4 pages, 8 figure

Coherent states, constraint classes, and area operators in the new spin-foam models

Recently, two new spin-foam models have appeared in the literature, both motivated by a desire to modify the Barrett-Crane model in such a way that the imposition of certain second class constraints, called cross-simplicity constraints, are weakened. We refer to these two models as the FKLS model, and the flipped model. Both of these models are based on a reformulation of the cross-simplicity constraints. This paper has two main parts. First, we clarify the structure of the reformulated cross-simplicity constraints and the nature of their quantum imposition in the new models. In particular we show that in the FKLS model, quantum cross-simplicity implies no restriction on states. The deeper reason for this is that, with the symplectic structure relevant for FKLS, the reformulated cross-simplicity constraints, in a certain relevant sense, are now \emph{first class}, and this causes the coherent state method of imposing the constraints, key in the FKLS model, to fail to give any restriction on states. Nevertheless, the cross-simplicity can still be seen as implemented via suppression of intertwiner degrees of freedom in the dynamical propagation. In the second part of the paper, we investigate area spectra in the models. The results of these two investigations will highlight how, in the flipped model, the Hilbert space of states, as well as the spectra of area operators exactly match those of loop quantum gravity, whereas in the FKLS (and Barrett-Crane) models, the boundary Hilbert spaces and area spectra are different.Comment: 21 pages; statements about gamma limits made more precise, and minor phrasing change

Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity

We give an independent derivation of the Engle-Pereira-Rovelli spinfoam model for quantum gravity which recently appeared in [arXiv:0705.2388]. Using the coherent state techniques introduced earlier in [arXiv:0705.0674], we show that the EPR model realizes a consistent imposition of the simplicity constraints implementing general relativity from a topological BF theory.Comment: 6 pages, 2 figures, v2: typos correcte

A New Spin Foam Model for 4d Gravity

Starting from Plebanski formulation of gravity as a constrained BF theory we propose a new spin foam model for 4d Riemannian quantum gravity that generalises the well-known Barrett-Crane model and resolves the inherent to it ultra-locality problem. The BF formulation of 4d gravity possesses two sectors: gravitational and topological ones. The model presented here is shown to give a quantization of the gravitational sector, and is dual to the recently proposed spin foam model of Engle et al. which, we show, corresponds to the topological sector. Our methods allow us to introduce the Immirzi parameter into the framework of spin foam quantisation. We generalize some of our considerations to the Lorentzian setting and obtain a new spin foam model in that context as well.Comment: 40 pages; (v2) published versio

LQG propagator: III. The new vertex

In the first article of this series, we pointed out a difficulty in the attempt to derive the low-energy behavior of the graviton two-point function, from the loop-quantum-gravity dynamics defined by the Barrett-Crane vertex amplitude. Here we show that this difficulty disappears when using the corrected vertex amplitude recently introduced in the literature. In particular, we show that the asymptotic analysis of the new vertex amplitude recently performed by Barrett, Fairbairn and others, implies that the vertex has precisely the asymptotic structure that, in the second article of this series, was indicated as the key necessary condition for overcoming the difficulty.Comment: 9 page

A Immirzi-like parameter for 3d quantum gravity

We study an Immirzi-like ambiguity in three-dimensional quantum gravity. It shares some features with the Immirzi parameter of four-dimensional loop quantum gravity: it does not affect the equations of motion, but modifies the Poisson brackets and the constraint algebra at the canonical level. We focus on the length operator and show how to define it through non-commuting fluxes. We compute its spectrum and show the effect of this Immirzi-like ambiguity. Finally, we extend these considerations to 4d gravity and show how the different topological modifications of the action affect the canonical structure of loop quantum gravity.Comment: 14 pages, v2: one reference added, more comments on the 3d/4d compariso

Encoding simplicial quantum geometry in group field theories

We show that a new symmetry requirement on the GFT field, in the context of an extended GFT formalism, involving both Lie algebra and group elements, leads, in 3d, to Feynman amplitudes with a simplicial path integral form based on the Regge action, to a proper relation between the discrete connection and the triad vectors appearing in it, and to a much more satisfactory and transparent encoding of simplicial geometry already at the level of the GFT action.Comment: 15 pages, 2 figures, RevTeX, references adde

Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory

We study the large-j asymptotics of the Euclidean EPRL/FK spin foam amplitude on a 4d simplicial complex with arbitrary number of simplices. We show that for a critical configuration (j_f, g_{ve}, n_{ef}) in general, there exists a partition of the simplicial complex into three regions: Non-degenerate region, Type-A degenerate region and Type-B degenerate region. On both the non-degenerate and Type-A degenerate regions, the critical configuration implies a non-degenerate Euclidean geometry, while on the Type-B degenerate region, the critical configuration implies a vector geometry. Furthermore we can split the Non-degenerate and Type-A regions into sub-complexes according to the sign of Euclidean oriented 4-simplex volume. On each sub-complex, the spin foam amplitude at critical configuration gives a Regge action that contains a sign factor sgn(V_4(v)) of the oriented 4-simplices volume. Therefore the Regge action reproduced here can be viewed as a discretized Palatini action with on-shell connection. The asymptotic formula of the spin foam amplitude is given by a sum of the amplitudes evaluated at all possible critical configurations, which are the products of the amplitudes associated to different type of geometries.Comment: 27 pages, 5 figures, references adde

Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory

A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we reconsider the implementation of the constraints that defines the model. We define in a simple way the boundary Hilbert space of the theory, introducing a slight modification of the embedding of the SU(2) representations into the SL(2,C) ones. We then show directly that all constraints vanish on this space in a weak sense. The vanishing is exact (and not just in the large quantum number limit.) We also generalize the definition of the volume operator in the spinfoam model to the Lorentzian signature, and show that it matches the one of loop quantum gravity, as does in the Euclidean case.Comment: 11 page