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  The Construction of Spin Foam Vertex Amplitudes

Bianchi, E., & Hellmann, F. (2013). The Construction of Spin Foam Vertex Amplitudes. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 9: 008. doi:10.3842/SIGMA.2013.008.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000E-9604-F Version Permalink: http://hdl.handle.net/11858/00-001M-0000-000E-9605-D
Genre: Journal Article

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1207.4596 (Preprint), 569KB
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 Creators:
Bianchi, Eugenio, Author
Hellmann, Frank1, Author              
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24014              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc
 Abstract: Spin foam vertex amplitudes are the key ingredient of spin foam models for quantum gravity. These fall into the realm of discretized path integral, and can be seen as generalized lattice gauge theories. They can be seen as an attempt at a 4-dimensional generalization of the Ponzano-Regge model for 3d quantum gravity. We motivate and review the construction of the vertex amplitudes of recent spin foam models, giving two different and complementary perspectives of this construction. The first proceeds by extracting geometric configurations from a topological theory of the BF type, and can be seen to be in the tradition of the work of Barrett, Crane, Freidel and Krasnov. The second keeps closer contact to the structure of Loop Quantum Gravity and tries to identify an appropriate set of constraints to define a Lorentz-invariant interaction of its quanta of space. This approach is in the tradition of the work of Smolin, Markopoulous, Engle, Pereira, Rovelli and Livine.

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 Dates: 2012-07-192013-01-312013
 Publication Status: Published in print
 Pages: 22
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 Rev. Method: -
 Identifiers: arXiv: 1207.4596
DOI: 10.3842/SIGMA.2013.008
URI: http://arxiv.org/abs/1207.4596
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Title: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Source Genre: Journal
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Pages: - Volume / Issue: 9 Sequence Number: 008 Start / End Page: - Identifier: -