Details
| Original language | English |
|---|---|
| Pages (from-to) | 10-19 |
| Number of pages | 10 |
| Journal | Journal of geometry and physics |
| Volume | 99 |
| Early online date | 28 Sept 2015 |
| Publication status | Published - Jan 2016 |
Abstract
We introduce the holonomy-diffeomorphism algebra, a C*-algebra generated by flows of vector fields and the compactly supported smooth functions on a manifold. We show that the separable representations of the holonomy-diffeomorphism algebra are given by measurable connections, and that the unitary equivalence of the representations corresponds to measured gauge equivalence of the measurable connections. We compare the setup to Loop Quantum Gravity and show that the generalized connections found there are not contained in the spectrum of the holonomy-diffeomorphism algebra in dimensions higher than one. This is the second paper of two, where the prequel gives an exposition of a framework of quantum gravity based on the holonomy-diffeomorphism algebra.
Keywords
- Ashtekar variables, Noncommutative geometry, Quantum gravity
ASJC Scopus subject areas
- Mathematics(all)
- Mathematical Physics
- Physics and Astronomy(all)
- General Physics and Astronomy
- Mathematics(all)
- Geometry and Topology
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In: Journal of geometry and physics, Vol. 99, 01.2016, p. 10-19.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - C*-algebras of holonomy-diffeomorphisms & quantum gravity II
AU - Aastrup, Johannes
AU - Grimstrup, Jesper Møller
PY - 2016/1
Y1 - 2016/1
N2 - We introduce the holonomy-diffeomorphism algebra, a C*-algebra generated by flows of vector fields and the compactly supported smooth functions on a manifold. We show that the separable representations of the holonomy-diffeomorphism algebra are given by measurable connections, and that the unitary equivalence of the representations corresponds to measured gauge equivalence of the measurable connections. We compare the setup to Loop Quantum Gravity and show that the generalized connections found there are not contained in the spectrum of the holonomy-diffeomorphism algebra in dimensions higher than one. This is the second paper of two, where the prequel gives an exposition of a framework of quantum gravity based on the holonomy-diffeomorphism algebra.
AB - We introduce the holonomy-diffeomorphism algebra, a C*-algebra generated by flows of vector fields and the compactly supported smooth functions on a manifold. We show that the separable representations of the holonomy-diffeomorphism algebra are given by measurable connections, and that the unitary equivalence of the representations corresponds to measured gauge equivalence of the measurable connections. We compare the setup to Loop Quantum Gravity and show that the generalized connections found there are not contained in the spectrum of the holonomy-diffeomorphism algebra in dimensions higher than one. This is the second paper of two, where the prequel gives an exposition of a framework of quantum gravity based on the holonomy-diffeomorphism algebra.
KW - Ashtekar variables
KW - Noncommutative geometry
KW - Quantum gravity
UR - http://www.scopus.com/inward/record.url?scp=84944706015&partnerID=8YFLogxK
U2 - 10.1016/j.geomphys.2015.09.007
DO - 10.1016/j.geomphys.2015.09.007
M3 - Article
AN - SCOPUS:84944706015
VL - 99
SP - 10
EP - 19
JO - Journal of geometry and physics
JF - Journal of geometry and physics
SN - 0393-0440
ER -