The Construction of Spin Foam Vertex Amplitudes

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 3...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2013
Main Authors: Bianchi, E., Hellmann, F.
Format: Article
Language:English
Published: Інститут математики НАН України 2013
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/149216
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:The Construction of Spin Foam Vertex Amplitudes / E. Bianchi, F. Hellmann // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 105 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Bianchi, E.
Hellmann, F.
author_facet Bianchi, E.
Hellmann, F.
citation_txt The Construction of Spin Foam Vertex Amplitudes / E. Bianchi, F. Hellmann // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 105 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description 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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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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language English
last_indexed 2025-12-07T20:12:58Z
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spelling Bianchi, E.
Hellmann, F.
2019-02-19T18:48:29Z
2019-02-19T18:48:29Z
2013
The Construction of Spin Foam Vertex Amplitudes / E. Bianchi, F. Hellmann // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 105 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 81T25; 81T45
DOI: http://dx.doi.org/10.3842/SIGMA.2013.008
https://nasplib.isofts.kiev.ua/handle/123456789/149216
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.
This paper is a contribution to the Special Issue “Loop Quantum Gravity and Cosmology”. The full collection is available at http://www.emis.de/journals/SIGMA/LQGC.html.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
The Construction of Spin Foam Vertex Amplitudes
Article
published earlier
spellingShingle The Construction of Spin Foam Vertex Amplitudes
Bianchi, E.
Hellmann, F.
title The Construction of Spin Foam Vertex Amplitudes
title_full The Construction of Spin Foam Vertex Amplitudes
title_fullStr The Construction of Spin Foam Vertex Amplitudes
title_full_unstemmed The Construction of Spin Foam Vertex Amplitudes
title_short The Construction of Spin Foam Vertex Amplitudes
title_sort construction of spin foam vertex amplitudes
url https://nasplib.isofts.kiev.ua/handle/123456789/149216
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