Intersecting Quantum Gravity with Noncommutative Geometry - a Review
We review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural noncommutative structures which have, hitherto, not been explored. Next, we present the construction of a spectral triple over an algebra of holo...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2012 |
| Hauptverfasser: | , |
| 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/123456789/148411 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Intersecting Quantum Gravity with Noncommutative Geometry - a Review / J. Aastrup, J.M. Grimstrup // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 51 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862744795043069952 |
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| author | Aastrup, J. Grimstrup, J.M. |
| author_facet | Aastrup, J. Grimstrup, J.M. |
| citation_txt | Intersecting Quantum Gravity with Noncommutative Geometry - a Review / J. Aastrup, J.M. Grimstrup // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 51 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural noncommutative structures which have, hitherto, not been explored. Next, we present the construction of a spectral triple over an algebra of holonomy loops. The spectral triple, which encodes the kinematics of quantum gravity, gives rise to a natural class of semiclassical states which entail emerging fermionic degrees of freedom. In the particular semiclassical approximation where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges. We end the paper with an extended outlook section.
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| first_indexed | 2025-12-07T20:36:46Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148411 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:36:46Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Aastrup, J. Grimstrup, J.M. 2019-02-18T11:52:21Z 2019-02-18T11:52:21Z 2012 Intersecting Quantum Gravity with Noncommutative Geometry - a Review / J. Aastrup, J.M. Grimstrup // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 51 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 46L52; 46L87; 46L89; 58B34; 81R60; 81T75; 83C65; 70S15 http://dx.doi.org/10.3842/SIGMA.2012.018 https://nasplib.isofts.kiev.ua/handle/123456789/148411 We review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural noncommutative structures which have, hitherto, not been explored. Next, we present the construction of a spectral triple over an algebra of holonomy loops. The spectral triple, which encodes the kinematics of quantum gravity, gives rise to a natural class of semiclassical states which entail emerging fermionic degrees of freedom. In the particular semiclassical approximation where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges. We end the paper with an extended outlook section. 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.
 We thank the referees for useful comments and suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Intersecting Quantum Gravity with Noncommutative Geometry - a Review Article published earlier |
| spellingShingle | Intersecting Quantum Gravity with Noncommutative Geometry - a Review Aastrup, J. Grimstrup, J.M. |
| title | Intersecting Quantum Gravity with Noncommutative Geometry - a Review |
| title_full | Intersecting Quantum Gravity with Noncommutative Geometry - a Review |
| title_fullStr | Intersecting Quantum Gravity with Noncommutative Geometry - a Review |
| title_full_unstemmed | Intersecting Quantum Gravity with Noncommutative Geometry - a Review |
| title_short | Intersecting Quantum Gravity with Noncommutative Geometry - a Review |
| title_sort | intersecting quantum gravity with noncommutative geometry - a review |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148411 |
| work_keys_str_mv | AT aastrupj intersectingquantumgravitywithnoncommutativegeometryareview AT grimstrupjm intersectingquantumgravitywithnoncommutativegeometryareview |