Learning about Quantum Gravity with a Couple of Nodes

Loop Quantum Gravity provides a natural truncation of the infinite degrees of freedom of gravity, obtained by studying the theory on a given finite graph. We review this procedure and we present the construction of the canonical theory on a simple graph, formed by only two nodes. We review the U(N) framework, which provides a powerful tool for the canonical study of this model, and a formulation of the system based on spinors. We consider also the covariant theory, which permits to derive the model from a more complex formulation, paying special attention to the cosmological interpretation of the theory

U(N) and holomorphic methods for LQG and Spin Foams

The U(N) framework and the spinor representation for loop quantum gravity are two new points of view that can help us deal with the most fundamental problems of the theory. Here, we review the detailed construction of the U(N) framework explaining how one can endow the Hilbert space of N-leg intertwiners with a Fock structure. We then give a description of the classical phase space corresponding to this system in terms of the spinors, and we will study its quantization using holomorphic techniques. We take special care in constructing the usual holonomy operators of LQG in terms of spinors, and in the description of the Hilbert space of LQG with the different polarization given by these spinors.Comment: 16 pages. Proceedings for the 3rd Quantum Geometry and Quantum Gravity School in Zakopane (2011

U(N) tools for Loop Quantum Gravity: The Return of the Spinor

We explore the classical setting for the U(N) framework for SU(2) intertwiners for loop quantum gravity (LQG) and describe the corresponding phase space in terms of spinors with appropriate constraints. We show how its quantization leads back to the standard Hilbert space of intertwiner states defined as holomorphic functionals. We then explain how to glue these intertwiners states in order to construct spin network states as wave-functions on the spinor phase space. In particular, we translate the usual loop gravity holonomy observables to our classical framework. Finally, we propose how to derive our phase space structure from an action principle which induces non-trivial dynamics for the spin network states. We conclude by applying explicitly our framework to states living on the simple 2-vertex graph and discuss the properties of the resulting Hamiltonian.Comment: 23 page

Measurement of the Higgs boson mass with the ATLAS detector

A summary of the latest results on the combined measurement of the Higgs boson mass in the H → ZZ* → 4l and the H → γγ decay channels with the ATLAS detector is presented. The analysis uses 25 fb−1 of pp collision data recorded by the ATLAS detector at the CERN Large Hadron Collider at centre-of-mass energies of 7TeV and 8 TeV during 2011 and 2012. The combined measured value of the Higgs boson mass is mH = 125.36 ± 0.37 (stat) ± 0.18 (syst) GeV

Global three-neutrino oscillation analysis of neutrino data

A global analysis of the solar, atmospheric and reactor neutrino data is presented in terms of three-neutrino oscillations. We include the most recent solar neutrino rates of Homestake, SAGE, GALLEX and GNO, as well as the recent 1117 day Super-Kamiokande data sample, including the recoil electron energy spectrum both for day and night periods and we treat in a unified way the full parameter space for oscillations, correctly accounting for the transition from the matter enhanced (MSW) to the vacuum oscillations regime. Likewise, we include in our description conversions with $\theta_{12} > \pi/4$. For the atmospheric data we perform our analysis of the contained events and the upward-going $\nu$-induced muon fluxes, including the previous data samples of Frejus, IMB, Nusex, and Kamioka experiments as well as the full 71 kton-yr (1144 days) Super-Kamiokande data set, the recent 5.1 kton-yr contained events of Soudan2 and the results on upgoing muons from the MACRO detector. We first present the allowed regions of solar and atmospheric oscillation parameters $\theta_{12}$, $\Delta m^2_{21}$ and $\theta_{23}$, $\Delta m^2_{32}$, respectively, as a function of $\theta_{13}$ and determine the constraints from atmospheric and solar data on the mixing angle $\theta_{13}$, common to solar and atmospheric analyses. We also obtain the allowed ranges of parameters from the full five-dimensional combined analysis of the solar, atmospheric and reactor data.Comment: 56 pages, 21 postscript figures. Some misprints corrected and new references added. Chooz limit included in Fig.21. Final version to appear in Phys. Rev.