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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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2012
Автори: Aastrup, J., Grimstrup, J.M.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2012
Онлайн доступ: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
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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-148411
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Intersecting Quantum Gravity with Noncommutative Geometry - a Review
spellingShingle Intersecting Quantum Gravity with Noncommutative Geometry - a Review
Aastrup, J.
Grimstrup, J.M.
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
author Aastrup, J.
Grimstrup, J.M.
author_facet Aastrup, J.
Grimstrup, J.M.
publishDate 2012
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.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.
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