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Author  |
Borja, E.F.; Diaz-Polo, J.; Garay, I.; Livine, E.R. |
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Title |
Dynamics for a 2-vertex quantum gravity model |
Type |
Journal Article |
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Year |
2010 |
Publication |
Classical and Quantum Gravity |
Abbreviated Journal |
Class. Quantum Gravity |
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Volume |
27 |
Issue |
23 |
Pages |
235010 - 34pp |
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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. |
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Address |
[Borja, Enrique F.; Garay, Inaki] Univ Erlangen Nurnberg, Inst Theoret Phys 3, D-91058 Erlangen, Germany, Email: etera.livine@ens-lyon.fr |
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Publisher |
Iop Publishing Ltd |
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English |
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ISSN |
0264-9381 |
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Notes |
ISI:000284211600011 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ elepoucu @ |
Serial |
341 |
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Author |
Borja, E.F.; Freidel, L.; Garay, I.; Livine, E.R. |
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Title |
U(N) tools for loop quantum gravity: the return of the spinor |
Type |
Journal Article |
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Year |
2011 |
Publication |
Classical and Quantum Gravity |
Abbreviated Journal |
Class. Quantum Gravity |
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Volume |
28 |
Issue |
5 |
Pages |
055005 - 28pp |
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Keywords |
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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. |
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Address |
[Borja, Enrique F.; Garay, Inaki] Univ Erlangen Nurnberg, Inst Theoret Phys 3, D-91058 Erlangen, Germany, Email: etera.livine@ens-lyon.fr |
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Publisher |
Iop Publishing Ltd |
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Language |
English |
Summary Language |
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ISSN |
0264-9381 |
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Notes |
ISI:000287308700005 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
579 |
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Author |
Borja, E.F.; Garay, I.; Strobel, E. |
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Title |
Revisiting the quantum scalar field in spherically symmetric quantum gravity |
Type |
Journal Article |
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Year |
2012 |
Publication |
Classical and Quantum Gravity |
Abbreviated Journal |
Class. Quantum Gravity |
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Volume |
29 |
Issue |
14 |
Pages |
145012 - 19pp |
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Keywords |
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Abstract |
We extend previous results in spherically symmetric gravitational systems coupled with a massless scalar field within the loop quantum gravity framework. As a starting point, we take the Schwarzschild spacetime. The results presented here rely on the uniform discretization method. We are able to minimize the associated discrete master constraint using a variational method. The trial state for the vacuum consists of a direct product of a Fock vacuum for the matter part and a Gaussian centered around the classical Schwarzschild solution. This paper follows the line of research presented by Gambini et al (2009 Class. Quantum Grav. 26 215011 (arXiv: 0906.1774v1)) and a comparison between their result and the one given in this work is made. |
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Address |
[Borja, Enrique F.; Garay, Inaki; Strobel, Eckhard] Univ Erlangen Nurnberg, Inst Theoret Phys 3, D-91058 Erlangen, Germany, Email: eckhard@bebsdb.dnsalias.net |
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Publisher |
Iop Publishing Ltd |
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Language |
English |
Summary Language |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
0264-9381 |
ISBN |
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Area |
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Expedition |
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Conference |
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Notes |
WOS:000305810600013 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
1087 |
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Author |
Borja, E.F.; Garay, I.; Vidotto, F. |
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Title |
Learning about Quantum Gravity with a Couple of Nodes |
Type |
Journal Article |
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Year |
2012 |
Publication |
Symmetry Integrability and Geometry-Methods and Applications |
Abbreviated Journal |
Symmetry Integr. Geom. |
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Volume |
8 |
Issue |
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Pages |
015 - 44pp |
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Keywords |
discrete gravity; canonical quantization; spinors; spinfoam; quantum cosmology |
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Abstract |
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. |
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Address |
[Borja, Enrique F.; Garay, Inaki] Univ Erlangen Nurnberg, Inst Theoret Phys 3, D-91058 Erlangen, Germany, Email: efborja@theorie3.physik.uni-erlangen.de; |
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Publisher |
Natl Acad Sci Ukraine, Inst Math |
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Language |
English |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
1815-0659 |
ISBN |
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Medium |
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Area |
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Expedition |
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Conference |
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Notes |
WOS:000303831400001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
1018 |
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