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SIGMA, 2012, Volume 8, 018, 25 pages (Mi sigma695)  

This article is cited in 5 scientific papers (total in 5 papers)

Intersecting quantum gravity with noncommutative geometry – a review

Johannes Aastrupa, Jesper Møller Grimstrupb

a Institut für Analysis, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
b Wildersgade 49b, 1408 Copenhagen, Denmark

Abstract: 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.

Keywords: quantum gravity, noncommutative geometry, semiclassical analysis.

DOI: https://doi.org/10.3842/SIGMA.2012.018

Full text: PDF file (498 kB)
Full text: http://emis.mi.ras.ru/.../018
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Bibliographic databases:

ArXiv: 1203.6164
MSC: 46L52; 46L87; 46L89; 58B34; 81R60; 81T75; 83C65; 70S15
Received: October 6, 2011; in final form March 16, 2012; Published online March 28, 2012
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Citation: Johannes Aastrup, Jesper Møller Grimstrup, “Intersecting quantum gravity with noncommutative geometry – a review”, SIGMA, 8 (2012), 018, 25 pp.

Citation in format AMSBIB
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\paper Intersecting quantum gravity with noncommutative geometry -- a review
\jour SIGMA
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\vol 8
\papernumber 018
\totalpages 25
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Aastrup J., Grimstrup J.M., “$C^*$-Algebras of Holonomy-Diffeomorphisms and Quantum Gravity: I”, Class. Quantum Gravity, 30:8 (2013), 085016  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Aastrup J., Grimstrup J.M., “$C^*$-Algebras of Holonomy-Diffeomorphisms & Quantum Gravity”, J. Geom. Phys., 99 (2016), 10–19  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Aastrup J., Grimstrup J.M., “Quantum holonomy theory”, Fortschritte Phys.-Prog. Phys., 64:10 (2016), 783–818  crossref  mathscinet  zmath  isi  scopus
    4. Aastrup J., Grimstrup J.M., “The quantum holonomy-diffeomorphism algebra and quantum gravity”, Int. J. Mod. Phys. A, 31:10 (2016), 1650048  crossref  mathscinet  zmath  isi  scopus
    5. Arici F., Stienstra R., van Suijlekom W.D., “Quantum Lattice Gauge Fields and Groupoid C-Algebras”, Ann. Henri Poincare, 19:11 (2018), 3241–3266  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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