820 research outputs found
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
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