Details
| Original language | English |
|---|---|
| Article number | 1650048 |
| Journal | International Journal of Modern Physics A |
| Volume | 31 |
| Issue number | 10 |
| Publication status | Published - 30 Mar 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.
Keywords
- noncommutative geometry, Quantum gravity, unification
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Physics and Astronomy(all)
- Astronomy and Astrophysics
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In: International Journal of Modern Physics A, Vol. 31, No. 10, 1650048, 30.03.2016.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The quantum holonomy-diffeomorphism algebra and quantum gravity
AU - Aastrup, Johannes
AU - Grimstrup, Jesper Møller
PY - 2016/3/30
Y1 - 2016/3/30
N2 - 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.
AB - 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.
KW - noncommutative geometry
KW - Quantum gravity
KW - unification
UR - http://www.scopus.com/inward/record.url?scp=84963636505&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1404.1500
DO - 10.48550/arXiv.1404.1500
M3 - Article
AN - SCOPUS:84963636505
VL - 31
JO - International Journal of Modern Physics A
JF - International Journal of Modern Physics A
SN - 0217-751X
IS - 10
M1 - 1650048
ER -