Spin Foams and Canonical Quantization
This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the two approaches are in good agreement, we show how the canonical quantization à la Witten of Riemannia...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2012 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2012
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148408 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Spin Foams and Canonical Quantization / S. Alexandrov, M. Geiller, K. Noui // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 150 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862750123750064128 |
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| author | Alexandrov, S. Geiller, M. Noui, K. |
| author_facet | Alexandrov, S. Geiller, M. Noui, K. |
| citation_txt | Spin Foams and Canonical Quantization / S. Alexandrov, M. Geiller, K. Noui // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 150 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the two approaches are in good agreement, we show how the canonical quantization à la Witten of Riemannian gravity with a positive cosmological constant is related to the Turaev-Viro spin foam model, and how the Ponzano-Regge amplitudes are related to the physical scalar product of Riemannian loop quantum gravity without cosmological constant. In the four-dimensional case, we recall a Lorentz-covariant formulation of loop quantum gravity using projected spin networks, compare it with the new spin foam models, and identify interesting relations and their pitfalls. Finally, we discuss the properties which a spin foam model is expected to possess in order to be consistent with the canonical quantization, and suggest a new model illustrating these results.
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| first_indexed | 2025-12-07T21:04:15Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148408 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:04:15Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Alexandrov, S. Geiller, M. Noui, K. 2019-02-18T11:45:24Z 2019-02-18T11:45:24Z 2012 Spin Foams and Canonical Quantization / S. Alexandrov, M. Geiller, K. Noui // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 150 назв. — англ. 1815-0659 https://nasplib.isofts.kiev.ua/handle/123456789/148408 This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the two approaches are in good agreement, we show how the canonical quantization à la Witten of Riemannian gravity with a positive cosmological constant is related to the Turaev-Viro spin foam model, and how the Ponzano-Regge amplitudes are related to the physical scalar product of Riemannian loop quantum gravity without cosmological constant. In the four-dimensional case, we recall a Lorentz-covariant formulation of loop quantum gravity using projected spin networks, compare it with the new spin foam models, and identify interesting relations and their pitfalls. Finally, we discuss the properties which a spin foam model is expected to possess in order to be consistent with the canonical quantization, and suggest a new model illustrating these results. 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.
 This research is supported by contract ANR-09-BLAN-0041. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Spin Foams and Canonical Quantization Article published earlier |
| spellingShingle | Spin Foams and Canonical Quantization Alexandrov, S. Geiller, M. Noui, K. |
| title | Spin Foams and Canonical Quantization |
| title_full | Spin Foams and Canonical Quantization |
| title_fullStr | Spin Foams and Canonical Quantization |
| title_full_unstemmed | Spin Foams and Canonical Quantization |
| title_short | Spin Foams and Canonical Quantization |
| title_sort | spin foams and canonical quantization |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148408 |
| work_keys_str_mv | AT alexandrovs spinfoamsandcanonicalquantization AT geillerm spinfoamsandcanonicalquantization AT nouik spinfoamsandcanonicalquantization |