Details
| Original language | English |
|---|---|
| Article number | 018 |
| Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |
| Volume | 8 |
| Publication status | Published - 28 Mar 2012 |
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
- Noncommutative geometry, Quantum gravity, Semiclassical analysis
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Mathematical Physics
- Mathematics(all)
- Geometry and Topology
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In: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), Vol. 8, 018, 28.03.2012.
Research output: Contribution to journal › Review article › Research › peer review
}
TY - JOUR
T1 - Intersecting quantum gravity with noncommutative geometry
T2 - A review
AU - Aastrup, Johannes
AU - Grimstrup, Jesper Møller
PY - 2012/3/28
Y1 - 2012/3/28
N2 - 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.
AB - 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.
KW - Noncommutative geometry
KW - Quantum gravity
KW - Semiclassical analysis
UR - http://www.scopus.com/inward/record.url?scp=84859417586&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1203.6164
DO - 10.48550/arXiv.1203.6164
M3 - Review article
AN - SCOPUS:84859417586
VL - 8
JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
SN - 1815-0659
M1 - 018
ER -