Emergence of gravity from spinfoams

We find a nontrivial regime of spinfoam quantum gravity that reproduces classical Einstein equations. This is the double scaling limit of small Immirzi parameter (gamma), large spins (j) with physical area (gamma times j) constant. In addition to quantum corrections in the Planck constant, we find new corrections in the Immirzi parameter due to the quantum discreteness of spacetime. The result is a strong evidence that the spinfoam covariant quantization of general relativity possesses the correct classical limit.Comment: 9 pages, shorter version of "Regge gravity from spinfoams

Regge gravity from spinfoams

We consider spinfoam quantum gravity for general triangulations in the regime $l_P^2\ll a\ll a/\gamma$, namely in the combined classical limit of large areas $a$ and flipped limit of small Barbero-Immirzi parameter $\gamma$, where $l_P$ is the Planck length. Under few working hypotheses we find that the flipped limit enforces the constraints that turn the spinfoam theory into an effective Regge-like quantum theory with lengths as variables, while the classical limit selects among the possible geometries the ones satisfying the Einstein equations. Two kinds of quantum corrections appear in terms of powers of $l^2_P/a$ and $\gamma l_P^2/a$. The result also suggests that the Barbero-Immirzi parameter may run to smaller values under coarse-graining of the triangulation.Comment: 18 pages, presentation substantially improve

On the geometry of curves and conformal geodesics in the Mobius space

This paper deals with the study of some properties of immersed curves in the conformal sphere \mathds{Q}_n, viewed as a homogeneous space under the action of the M\"obius group. After an overview on general well-known facts, we briefly focus on the links between Euclidean and conformal curvatures, in the spirit of F. Klein's Erlangen program. The core of the paper is the study of conformal geodesics, defined as the critical points of the conformal arclength functional. After writing down their Euler-Lagrange equations for any $n$, we prove an interesting codimension reduction, namely that every conformal geodesic in \mathds{Q}_n lies, in fact, in a totally umbilical 4-sphere \mathds{Q}_4. We then extend and complete the work in (Musso, "The conformal arclength functional", Math Nachr.) by solving the Euler-Lagrange equations for the curvatures and by providing an explicit expression even for those conformal geodesics not included in any conformal 3-sphere.Comment: 40 page

Fractal Space-Time from Spin-Foams

In this paper we perform the calculation of the spectral dimension of spacetime in 4d quantum gravity using the Barrett-Crane (BC) spinfoam model. We realize this considering a very simple decomposition of the 4d spacetime already used in the graviton propagator calculation and we introduce a boundary state which selects a classical geometry on the boundary. We obtain that the spectral dimension of the spacetime runs from $\approx 2$ to 4, across a $\approx 1.5$ phase, when the energy of a probe scalar field decreases from high $E \lesssim E_P/25$ to low energy. The spectral dimension at the Planck scale $E \approx E_P$ depends on the areas spectrum used in the calculation. For three different spectra $l_P^2 \sqrt{j(j+1)}$, $l_P^2 (2 j+1)$ and $l_P^2 j$ we find respectively dimension $\approx 2.31$, 2.45 and 2.08.Comment: 5 pages, 2 figure

Coherent spin-networks

In this paper we discuss a proposal of coherent states for Loop Quantum Gravity. These states are labeled by a point in the phase space of General Relativity as captured by a spin-network graph. They are defined as the gauge invariant projection of a product over links of Hall's heat-kernels for the cotangent bundle of SU(2). The labels of the state are written in terms of two unit-vectors, a spin and an angle for each link of the graph. The heat-kernel time is chosen to be a function of the spin. These labels are the ones used in the Spin Foam setting and admit a clear geometric interpretation. Moreover, the set of labels per link can be written as an element of SL(2,C). Therefore, these states coincide with Thiemann's coherent states with the area operator as complexifier. We study the properties of semiclassicality of these states and show that, for large spins, they reproduce a superposition over spins of spin-networks with nodes labeled by Livine-Speziale coherent intertwiners. Moreover, the weight associated to spins on links turns out to be given by a Gaussian times a phase as originally proposed by Rovelli.Comment: 15 page

Computer self-efficacy beliefs of preservice teachers: Implementation of a concurrent mixed-model.

This aim of this concurrent nested mixed-model study was to examine the computer self-efficacy beliefs of 210 preservice teachers. The quantitative component consisted of the Computer User Self-Efficacy (CUSE) scale that examined the relationship between computer self-efficacy and gender, age, ethnic origin, previous undergraduate degree, licensure area, software packages use, computer experience, training, ownership and socioeconomic status of preservice teachers. Students\u27 previous undergraduate degree, licensure area, experience and familiarity with software packages were found to have a statistically significant effect on computer self-efficacy. The qualitative data indicated that society and school were the most positive factors that influenced preservice teachers\u27 attitudes towards computers, while the family had the highest percentage of negative influence. The findings revealed that although preservice teachers had completed only two months of the program, those with higher CUSE scores were more ready to integrate computers into their lessons than those with lower scores. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2006 .M36. Source: Masters Abstracts International, Volume: 45-01, page: 0070. Thesis (M.Ed.)--University of Windsor (Canada), 2006