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Author (up) Borja, E.F.; Diaz-Polo, J.; Garay, I.; Livine, E.R. url  doi
openurl 
  Title Dynamics for a 2-vertex quantum gravity model Type Journal Article
  Year 2010 Publication Classical and Quantum Gravity Abbreviated Journal Class. Quantum Gravity  
  Volume 27 Issue 23 Pages 235010 - 34pp  
  Keywords  
  Abstract We use the recently introduced U(N) framework for loop quantum gravity to study the dynamics of spin network states on the simplest class of graphs: two vertices linked with an arbitrary number N of edges. Such graphs represent two regions, in and out, separated by a boundary surface. We study the algebraic structure of the Hilbert space of spin networks from the U(N) perspective. In particular, we describe the algebra of operators acting on that space and discuss their relation to the standard holonomy operator of loop quantum gravity. Furthermore, we show that it is possible to make the restriction to the isotropic/homogeneous sector of the model by imposing the invariance under a global U(N) symmetry. We then propose a U(N)-invariant Hamiltonian operator and study the induced dynamics. Finally, we explore the analogies between this model and loop quantum cosmology and sketch some possible generalizations of it.  
  Address [Borja, Enrique F.; Garay, Inaki] Univ Erlangen Nurnberg, Inst Theoret Phys 3, D-91058 Erlangen, Germany, Email: etera.livine@ens-lyon.fr  
  Corporate Author Thesis  
  Publisher Iop Publishing Ltd Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0264-9381 ISBN Medium  
  Area Expedition Conference  
  Notes ISI:000284211600011 Approved no  
  Is ISI yes International Collaboration yes  
  Call Number IFIC @ elepoucu @ Serial 341  
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Author (up) Borja, E.F.; Freidel, L.; Garay, I.; Livine, E.R. url  doi
openurl 
  Title U(N) tools for loop quantum gravity: the return of the spinor Type Journal Article
  Year 2011 Publication Classical and Quantum Gravity Abbreviated Journal Class. Quantum Gravity  
  Volume 28 Issue 5 Pages 055005 - 28pp  
  Keywords  
  Abstract We explore the classical setting for the U(N) framework for SU(2) intertwiners for loop quantum gravity and describe the corresponding phase space in terms of spinors with the 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 wavefunctions 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.  
  Address [Borja, Enrique F.; Garay, Inaki] Univ Erlangen Nurnberg, Inst Theoret Phys 3, D-91058 Erlangen, Germany, Email: etera.livine@ens-lyon.fr  
  Corporate Author Thesis  
  Publisher Iop Publishing Ltd Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0264-9381 ISBN Medium  
  Area Expedition Conference  
  Notes ISI:000287308700005 Approved no  
  Is ISI yes International Collaboration yes  
  Call Number IFIC @ pastor @ Serial 579  
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