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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| Дата: | 2012 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2012
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148411 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1484112019-02-19T01:30:11Z Intersecting Quantum Gravity with Noncommutative Geometry - a Review Aastrup, J. Grimstrup, J.M. 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. 2012 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/148411 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Aastrup, J. Grimstrup, J.M. |
| spellingShingle |
Aastrup, J. Grimstrup, J.M. Intersecting Quantum Gravity with Noncommutative Geometry - a Review Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Aastrup, J. Grimstrup, J.M. |
| author_sort |
Aastrup, J. |
| title |
Intersecting Quantum Gravity with Noncommutative Geometry - a Review |
| title_short |
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_sort |
intersecting quantum gravity with noncommutative geometry - a review |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148411 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT aastrupj intersectingquantumgravitywithnoncommutativegeometryareview AT grimstrupjm intersectingquantumgravitywithnoncommutativegeometryareview |
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2023-05-20T17:30:28Z |
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2023-05-20T17:30:28Z |
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1796153448402518016 |