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  Effective Hamiltonian Constraint from Group Field Theory

Livine, E. R., Oriti, D., & Ryan, J. P. (2011). Effective Hamiltonian Constraint from Group Field Theory. Classical and quantum gravity, 28(24): 245010. doi:10.1088/0264-9381/28/24/245010.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-30F7-F Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-30FA-9
Genre: Journal Article

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1104.5509 (Preprint), 271KB
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 Creators:
Livine, Etera R., Author
Oriti, Daniele1, Author              
Ryan, James P.2, Author              
Affiliations:
1Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_67201              
2Canonical 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
 Abstract: Spinfoam models provide a covariant formulation of the dynamics of loop quantum gravity. They are non-perturbatively defined in the group field theory (GFT) framework: the GFT partition function defines the sum of spinfoam transition amplitudes over all possible (discretized) geometries and topologies. The issue remains, however, of explicitly relating the specific form of the group field theory action and the canonical Hamiltonian constraint. Here, we suggest an avenue for addressing this issue. Our strategy is to expand group field theories around non-trivial classical solutions and to interpret the induced quadratic kinematical term as defining a Hamiltonian constraint on the group field and thus on spin network wave functions. We apply our procedure to Boulatov group field theory for 3d Riemannian gravity. Finally, we discuss the relevance of understanding the spectrum of this Hamiltonian operator for the renormalization of group field theories.

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 Dates: 2011-04-282011
 Publication Status: Published in print
 Pages: 14 pages
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1104.5509
DOI: 10.1088/0264-9381/28/24/245010
 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: 28 (24) Sequence Number: 245010 Start / End Page: - Identifier: ISSN: 0264-9381
CoNE: https://pure.mpg.de/cone/journals/resource/954925513480_1