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

Twisted geometries: A geometric parametrisation of SU(2) phase space

A cornerstone of the loop quantum gravity program is the fact that the phase space of general relativity on a fixed graph can be described by a product of SU(2) cotangent bundles per edge. In this paper we show how to parametrize this phase space in terms of quantities describing the intrinsic and extrinsic geometry of the triangulation dual to the graph. These are defined by the assignment to each triangle of its area, the two unit normals as seen from the two polyhedra sharing it, and an additional angle related to the extrinsic curvature. These quantities do not define a Regge geometry, since they include extrinsic data, but a looser notion of discrete geometry which is twisted in the sense that it is locally well-defined, but the local patches lack a consistent gluing among each other. We give the Poisson brackets among the new variables, and exhibit a symplectomorphism which maps them into the Poisson brackets of loop gravity. The new parametrization has the advantage of a simple description of the gauge-invariant reduced phase space, which is given by a product of phase spaces associated to edges and vertices, and it also provides an abelianisation of the SU(2) connection. The results are relevant for the construction of coherent states, and as a byproduct, contribute to clarify the connection between loop gravity and its subset corresponding to Regge geometries.Comment: 28 pages. v2 and v3 minor change

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

A near-wall two-equation model for compressible turbulent flows

A near-wall two-equation turbulence model of the K - epsilon type is developed for the description of high-speed compressible flows. The Favre-averaged equations of motion are solved in conjunction with modeled transport equations for the turbulent kinetic energy and solenoidal dissipation wherein a variable density extension of the asymptotically consistent near-wall model of So and co-workers is supplemented with new dilatational models. The resulting compressible two-equation model is tested in the supersonic flat plate boundary layer - with an adiabatic wall and with wall cooling - for Mach numbers as large as 10. Direct comparisons of the predictions of the new model with raw experimental data and with results from the K - omega model indicate that it performs well for a wide range of Mach numbers. The surprising finding is that the Morkovin hypothesis, where turbulent dilatational terms are neglected, works well at high Mach numbers, provided that the near wall model is asymptotically consistent. Instances where the model predictions deviate from the experiments appear to be attributable to the assumption of constant turbulent Prandtl number - a deficiency that will be addressed in a future paper

On the Generalized Einstein-Cartan Action with Fermions

From the freedom exhibited by the generalized Einstein action proposed in [1], we show that we can construct the standard effective Einstein-Cartan action coupled to the fermionic matter without the usual current-current interaction and therefore an effective action which does not depend neither on the Immirzi parameter nor on the torsion. This establishes the equivalence between the Einstein-Cartan theory and the theory of the general relativity minimally coupled to the fermionic matter.Comment: 8 pages, Added references, Corrected typos, Accepted in Class. Quant. Gra

Unification of gravity, gauge fields, and Higgs bosons

We consider a diffeomorphism invariant theory of a gauge field valued in a Lie algebra that breaks spontaneously to the direct sum of the spacetime Lorentz algebra, a Yang-Mills algebra, and their complement. Beginning with a fully gauge invariant action -- an extension of the Plebanski action for general relativity -- we recover the action for gravity, Yang-Mills, and Higgs fields. The low-energy coupling constants, obtained after symmetry breaking, are all functions of the single parameter present in the initial action and the vacuum expectation value of the Higgs.Comment: 12 pages, no figures. v2 minor correction

The role of minimal access valve surgery in the elderly. A meta-analysis of observational studies

Background Minimal access valve surgery, both mitral and aortic, may be related to improvement in specific post-operative outcomes, therefore may be beneficial for the subgroup of the elderly referred for valve surgery. Methods A systematic literature review identified several different studies, of which 6 fulfilled criteria for meta-analysis. Outcomes for a total of 1347 patients (675 conventional standard sternotomy and 672 minimally invasive valve surgery) were assessed with a meta-analysis using random effects modeling. Heterogeneity, subgroup analysis with quality scoring were also assessed. The primary endpoint was early mortality. Secondary endpoints included intra and post-operative outcomes. Results In the context of elderly patients, minimal access valve surgery conferred comparable early mortality to standard sternotomy (odd ratio (OR) 0.79, CI [0.40,1.56], p\ua0=\ua00.50) with no heterogeneity (p\ua0=\ua00.13); it was also associated with reduced mechanical intubation time (OR 0.48, CI [0.30,0.78], p\ua0=\ua00.003) and reduced post-operative length of stay (weighted mean difference (WMD)\ua0 122.91, CI [ 123.09,\ua0 122.74] p\ua0<\ua00.00001), however both cardio-pulmonary bypass time and cross clamp time were longer (WMD 24.29, CI [22.97, 25.61] p\ua0<\ua00.00001 and WMD 8.61, CI [7.61, 9.61], p\ua0<\ua00.00001, respectively); subgroup analysis demonstrated statistically significant reduced post-operative length of stay for both minimally invasive aortic and mitral surgery (WMD\ua0 122.84, CI [ 123.07,\ua0 122.60] p\ua0<\ua00.00001 and WMD\ua0 122.98, CI [ 123.25,\ua0 122.71] p\ua0<\ua00.00001 respectively). Conclusions Despite a prolonged cardiopulmonary bypass and cross clamp time, minimally invasive valve surgery is a safe alternative to standard sternotomy in the elderly, with similar early mortality, and improvements in intubation time as well as length of stay

Effects of hydrostaticity on the structural stability of carbonates at lower mantle pressures the case study of dolomite

We have conducted high pressure far-infrared absorbance and Raman spectroscopic investigations on a natural iron-free dolomite sample up to 40 GPa. Comparison between the present observations and literature results unraveled the effect of hydrostatic conditions on the high pressure dolomite polymorph adopted close to 40 GPa, i.e. the triclinic Dol-IIIc modification. In particular, non-hydrostatic conditions impose structural disorder at these pressures, whereas hydrostatic conditions allow the detection of an ordered Dol-IIIc vibrational response. Hence, hydrostatic conditions appear to be a key ingredient for modeling carbon subduction at lower mantle conditions. Our complementary first-principles calculations verified the far-infrared vibrational response of the ambient- and high pressure dolomite phases.This study was partly supported by a Grant from Deutsche Forschungsgemeinschaft (DFG) within the Research Unit FOR2125 CarboPaT under Grants KO1260/16 and JA1469/9