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

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

Towards the graviton from spinfoams: higher order corrections in the 3d toy model

We consider the recent calculation gr-qc/0508124 of the graviton propagator in the spinfoam formalism. Within the 3d toy model introduced in gr-qc/0512102, we test how the spinfoam formalism can be used to construct the perturbative expansion of graviton amplitudes. Although the 3d graviton is a pure gauge, one can choose to work in a gauge where it is not zero and thus reproduce the structure of the 4d perturbative calculations. We compute explicitly the next to leading and next to next to leading orders, corresponding to one-loop and two-loop corrections. We show that while the first arises entirely from the expansion of the Regge action around the flat background, the latter receives contributions from the microscopic, non Regge-like, quantum geometry. Surprisingly, this new contribution reduces the magnitude of the next to next to leading order. It thus appears that the spinfoam formalism is likely to substantially modify the conventional perturbative expansion at higher orders. This result supports the interest in this approach. We then address a number of open issues in the rest of the paper. First, we discuss the boundary state ansatz, which is a key ingredient in the whole construction. We propose a way to enhance the ansatz in order to make the edge lengths and dihedral angles conjugate variables in a mathematically well-defined way. Second, we show that the leading order is stable against different choices of the face weights of the spinfoam model; the next to leading order, on the other hand, is changed in a simple way, and we show that the topological face weight minimizes it. Finally, we extend the leading order result to the case of a regular, but not equilateral, tetrahedron.Comment: 24 pages, many figure

Towards the graviton from spinfoams: the 3d toy model

Recently, a proposal has appeared for the extraction of the 2-point function of linearised quantum gravity, within the spinfoam formalism. This relies on the use of a boundary state, which introduces a semi-classical flat geometry on the boundary. In this paper, we investigate this proposal considering a toy model in the (Riemannian) 3d case, where the semi-classical limit is better understood. We show that in this limit the propagation kernel of the model is the one for the harmonic oscillator. This is at the origin of the expected 1/L behaviour of the 2-point function. Furthermore, we numerically study the short scales regime, where deviations from this behaviour occur.Comment: 8 pages, 2 figures; v3 revised versio

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

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

Early Carotid Endarterectomy after Ischemic Stroke: The Results of a Prospective Multicenter Italian Study

ObjectivesTo evaluate safety of early carotid endarterectomy (CEA) in patients with acute brain ischemia presenting to the emergency department stroke units (EDSU).MethodsThe neurologists, neuroradiologists and vascular surgeons on duty in emergency departments enrolled 96 patients who underwent very early CEA according to a predefined protocol within two years. The protocol included evaluation of neurological status by National Institute of Health Stroke Scale (NIHSS), neuroimaging assessment, ultrasound of the carotid arteries and Transcranial Doppler. Patients with NIHSS>22 or whose neuroimaging showed brain infarct >2/3 of the middle cerebral artery territory were excluded. All eligible patients underwent CEA as soon as possible. Primary end points of the study were mortality, neurological morbidity by NIHSS and postoperative hemorrhagic conversion on neuroimaging. Statistical analysis was performed by univariate analysis.ResultsThe mean time elapsing between the onset of stroke and endarterectomy was 1.5 days (±2 days). The overall 30-day morbidity mortality rate was 7.3% (7/96). No neurological mortality occurred. On hospital discharge, three patients (3%) experienced worsening of the neurological deficit (NIHSS score 1 to 2, 1 to 3 and 9 to 10 respectively). Postoperative CT demonstrated there were no new cerebral infarcts nor hemorrhagic transformation. At hospital discharge 9/96 patients (9%) had no improvement in NHISS scores, 37 were asymptomatic and 45 showed a median decrease of 4.5 NIHSS points (range 1–18). By univariate analysis none of the considered variables influenced the clinical outcome.ConclusionOur protocol selected patients who can safely undergo very early (<1.5 days) surgery after acute brain ischemia. Large randomized multicenter prospective trials are warranted to compare very early CEA versus best medical therapy

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