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Keywords
(2)
Quantum Gravity
Spectral Triple
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A New Spectral Triple over a Space of Connections
A New Spectral Triple over a Space of Connections,10.1007/s0022000907588,Communications in Mathematical Physics,Johannes Aastrup,Jesper Møller Grim
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A New Spectral Triple over a Space of Connections
(
Citations: 10
)
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Johannes Aastrup
,
Jesper Møller Grimstrup
,
Ryszard Nest
A new construction of a semifinite
spectral triple
on an algebra of holonomy loops is presented. The construction is canonically associated to
quantum gravity
and is an alternative version of the
spectral triple
presented in [1].
Journal:
Communications in Mathematical Physics  COMMUN MATH PHYS
, vol. 290, no. 1, pp. 389398, 2009
DOI:
10.1007/s0022000907588
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Citation Context
(3)
...Its existence  as a mathematical entity  was established in [4,
5
]...
...In [
5
] it was clear that the construction would work for a large class of such systems of graphs and no...
...In this section we outline the construction of the semifinite spectral triple first presented in [3,4] and further developed in [
5
]...
...However, for reasons explained in [
5
] it turns out that D1 and D � should of the form...
...The change of variables in (8) is the key step to construct D� n . However, there will be many different partitions of the line segment which simplify the structure maps and lead to different Dirac type operators, see Fig. 4. This ambiguity was also commented on in [
5
]...
Johannes Aastrup
,
et al.
On SemiClassical States of Quantum Gravity and Noncommutative Geometry
...As a fully geometrical theory (the action depends only on the eigenvalues of the Dirac operator and so it is pure geometry and diffeomorphism invariant) its quantisation would involve quantum gravity in some sense [
1
]...
...Aastrup, Grimstrup and Nest [
1
],[2] already established a link between Connes’s noncommutative geometry and loop quantum gravity...
...Instead of ~ always taking a certain value, it is viewed as a continuous parameter taking values in an interval of the real line [0,
1
] and the classical limit is obtained as it ‘goes to zero’...
R. A. DAWE MARTINS
.
CATEGORIFIED NONCOMMUTATIVE MANIFOLDS
...As a fully geometrical theory (the action depends only on the eigenvalues of the Dirac operator and so it is pure geometry and diffeomorphism invariant) its quantisation would involve quantum gravity in some sense [
1
]...
...Aastrup, Grimstrup and Nest [
1
],[2] already established a link between Connes’s noncommutative geometry and loop quantum gravity...
...Instead of ~ always taking a certain value, it is viewed as a continuous parameter taking values in an interval of the real line [0,
1
] and the classical limit is obtained as it ‘goes to zero’...
R. A. Dawe Martins
.
Some constructions in Category theory and Noncommutative geometry
References
(9)
Spectral Triples of Holonomy Loops
(
Citations: 10
)
Johannes Aastrup
,
Jesper Møller Grimstrup
Journal:
Communications in Mathematical Physics  COMMUN MATH PHYS
, vol. 264, no. 3, pp. 657681, 2006
Intersecting Connes Noncommutative Geometry with Quantum Gravity
(
Citations: 11
)
Johannes Aastrup
,
Jesper Møller Grimstrup
Journal:
International Journal of Modern Physics A  IJMPA
, vol. 22, no. 8 & 9, pp. 15891603, 2007
Representation Theory of Analytic Holonomy C* Algebras
(
Citations: 133
)
Abhay Ashtekar
,
Jerzy Lewandowski
Published in 1993.
TOPICAL REVIEW: Background independent quantum gravity: a status report
(
Citations: 333
)
Abhay Ashtekar
,
Jerzy Lewandowski
Journal:
Classical and Quantum Gravity  CLASS QUANTUM GRAVITY
, vol. 21, no. 15, pp. 53R152, 2004
Separable Hilbert space in loop quantum gravity
(
Citations: 38
)
Winston Fairbairn
,
Carlo Rovelli
Published in 2004.
Sort by:
Citations
(10)
On SemiClassical States of Quantum Gravity and Noncommutative Geometry
(
Citations: 6
)
Johannes Aastrup
,
Jesper Møller Grimstrup
,
Mario Paschke
,
Ryszard Nest
Journal:
Communications in Mathematical Physics  COMMUN MATH PHYS
, vol. 302, no. 3, pp. 675696, 2011
Spin foams and noncommutative geometry
(
Citations: 1
)
Domenic Denicola
,
Matilde Marcolli
,
Ahmad Zainy alYasry
Journal:
Classical and Quantum Gravity  CLASS QUANTUM GRAVITY
, vol. 27, no. 20, 2010
On a Derivation of the Dirac Hamiltonian From a Construction of Quantum Gravity
(
Citations: 1
)
Johannes Aastrup
,
Jesper M. Grimstrup
,
Mario Paschke
Published in 2010.
Modular Theory, NonCommutative Geometry and Quantum Gravity
Paolo Bertozzini
,
Roberto Conti
,
Wicharn Lewkeeratiyutkul
Journal:
Symmetry Integrability and Geometrymethods and Applications  SYMMETRY INTEGR GEOM
, 2010
The JLO Character for The Noncommutative Space of Connections of AastrupGrimstrupNest
Alan Lai
Published in 2010.