| Records |
Author  |
Borja, E.F.; Diaz-Polo, J.; Garay, I.; Livine, E.R. |
| 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 |
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Thesis |
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| Publisher |
Iop Publishing Ltd |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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| Series Editor |
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Series Title |
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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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Medium |
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| Area |
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Expedition |
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Conference |
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| Notes |
ISI:000284211600011 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ elepoucu @ |
Serial |
341 |
| Permanent link to this record |
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| Author |
Borja, E.F.; Freidel, L.; Garay, I.; Livine, E.R. |
| 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 |
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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. |
| 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 |
| Permanent link to this record |
