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The quantum holonomy-diffeomorphism algebra and quantum gravity

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OriginalspracheEnglisch
Aufsatznummer1650048
FachzeitschriftInternational Journal of Modern Physics A
Jahrgang31
Ausgabenummer10
PublikationsstatusVeröffentlicht - 30 März 2016

Abstract

We introduce the quantum holonomy-diffeomorphism ∗-algebra, which is generated by holonomy-diffeomorphisms on a three-dimensional manifold and translations on a space of SU(2)-connections. We show that this algebra encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Furthermore, we show that semiclassical states exist on the holonomy-diffeomorphism part of the algebra but that these states cannot be extended to the full algebra. Via a Dirac-type operator we derive a certain class of unbounded operators that act in the GNS construction of the semiclassical states. These unbounded operators are the type of operators, which we have previously shown to entail the spatial three-dimensional Dirac operator and Dirac-Hamiltonian in a semiclassical limit. Finally, we show that the structure of the Hamilton constraint emerges from a Yang-Mills-type operator over the space of SU(2)-connections.

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The quantum holonomy-diffeomorphism algebra and quantum gravity. / Aastrup, Johannes; Grimstrup, Jesper Møller.
in: International Journal of Modern Physics A, Jahrgang 31, Nr. 10, 1650048, 30.03.2016.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Aastrup J, Grimstrup JM. The quantum holonomy-diffeomorphism algebra and quantum gravity. International Journal of Modern Physics A. 2016 Mär 30;31(10):1650048. doi: 10.48550/arXiv.1404.1500, 10.1142/S0217751X16500482
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