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  Classical Setting and Effective Dynamics for Spinfoam Cosmology

Livine, E. R., & Martin-Benito, M. (2013). Classical Setting and Effective Dynamics for Spinfoam Cosmology. Classical and quantum gravity, 30(3): 035006. doi:10.1088/0264-9381/30/3/035006.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-51A4-9 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0015-1987-5
Genre: Journal Article

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1111.2867 (Preprint), 991KB
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 Creators:
Livine, Etera R., Author
Martin-Benito, Mercedes1, Author              
Affiliations:
1Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_102878              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th
 Abstract: We explore how to extract effective dynamics from loop quantum gravity and spinfoams truncated to a finite fixed graph, with the hope of modeling symmetry-reduced gravitational systems. We particularize our study to the 2-vertex graph with N links. We describe the canonical data using the recent formulation of the phase space in terms of spinors, and implement a symmetry-reduction to the homogeneous and isotropic sector. From the canonical point of view, we construct a consistent Hamiltonian for the model and discuss its relation with Friedmann-Robertson-Walker cosmologies. Then, we analyze the dynamics from the spinfoam approach. We compute exactly the transition amplitude between initial and final coherent spin networks states with support on the 2-vertex graph, for the choice of the simplest two-complex (with a single space-time vertex). The transition amplitude verifies an exact differential equation that agrees with the Hamiltonian constructed previously. Thus, in our simple setting we clarify the link between the canonical and the covariant formalisms.

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 Dates: 2011-11-112013
 Publication Status: Published in print
 Pages: 38 pages
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1111.2867
DOI: 10.1088/0264-9381/30/3/035006
 Degree: -

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Title: Classical and quantum gravity
Source Genre: Journal
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Publ. Info: Bristol, U.K. : Institute of Physics
Pages: - Volume / Issue: 30 (3) Sequence Number: 035006 Start / End Page: - Identifier: ISSN: 0264-9381
CoNE: /journals/resource/954925513480_1