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 |
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| Date: | 2013 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2013
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| 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| _version_ | 1862740249931677696 |
|---|---|
| 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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| first_indexed | 2025-12-07T20:12:58Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149216 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:12:58Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| 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 |
| work_keys_str_mv | AT bianchie theconstructionofspinfoamvertexamplitudes AT hellmannf theconstructionofspinfoamvertexamplitudes AT bianchie constructionofspinfoamvertexamplitudes AT hellmannf constructionofspinfoamvertexamplitudes |