On the geometry of loop quantum gravity on a graph

We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the "twisted geometries" and derive a simple relation between these and Regge geometries.Comment: 6 pages, 1 figure. v2: some typos corrected, references update

A semiclassical tetrahedron

We construct a macroscopic semiclassical state state for a quantum tetrahedron. The expectation values of the geometrical operators representing the volume, areas and dihedral angles are peaked around assigned classical values, with vanishing relative uncertainties.Comment: 10 pages; v2 revised versio

Grasping rules and semiclassical limit of the geometry in the Ponzano-Regge model

We show how the expectation values of geometrical quantities in 3d quantum gravity can be explicitly computed using grasping rules. We compute the volume of a labelled tetrahedron using the triple grasping. We show that the large spin expansion of this value is dominated by the classical expression, and we study the next to leading order quantum corrections.Comment: 18 pages, 1 figur

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

A new spinfoam vertex for quantum gravity

We introduce a new spinfoam vertex to be used in models of 4d quantum gravity based on SU(2) and SO(4) BF theory plus constraints. It can be seen as the conventional vertex of SU(2) BF theory, the 15j symbol, in a particular basis constructed using SU(2) coherent states. This basis makes the geometric interpretation of the variables transparent: they are the vectors normal to the triangles within each tetrahedron. We study the condition under which these states can be considered semiclassical, and we show that the semiclassical ones dominate the evaluation of quantum correlations. Finally, we describe how the constraints reducing BF to gravity can be directly written in terms of the new variables, and how the semiclassicality of the states might improve understanding the correct way to implement the constraints.Comment: 17+8 pages, 6 figures. v2 updated reference

Graviton propagator in loop quantum gravity

We compute some components of the graviton propagator in loop quantum gravity, using the spinfoam formalism, up to some second order terms in the expansion parameter.Comment: 41 pages, 6 figure

Coupling gauge theory to spinfoam 3d quantum gravity

We construct a spinfoam model for Yang-Mills theory coupled to quantum gravity in three dimensional riemannian spacetime. We define the partition function of the coupled system as a power series in g_0^2 G that can be evaluated order by order using grasping rules and the recoupling theory. With respect to previous attempts in the literature, this model assigns the dynamical variables of gravity and Yang-Mills theory to the same simplices of the spinfoam, and it thus provides transition amplitudes for the spin network states of the canonical theory. For SU(2) Yang-Mills theory we show explicitly that the partition function has a semiclassical limit given by the Regge discretization of the classical Yang-Mills action.Comment: 18 page

Area-angle variables for general relativity

We introduce a modified Regge calculus for general relativity on a triangulated four dimensional Riemannian manifold where the fundamental variables are areas and a certain class of angles. These variables satisfy constraints which are local in the triangulation. We expect the formulation to have applications to classical discrete gravity and non-perturbative approaches to quantum gravity.Comment: 7 pages, 1 figure. v2 small changes to match published versio

A Note on B-observables in Ponzano-Regge 3d Quantum Gravity

We study the insertion and value of metric observables in the (discrete) path integral formulation of the Ponzano-Regge spinfoam model for 3d quantum gravity. In particular, we discuss the length spectrum and the relation between insertion of such B-observables and gauge fixing in the path integral.Comment: 17 page