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Keywords
(2)
Quantum Gravity
Spectral Triple
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On spectral triples in quantum gravity II
On spectral triples in quantum gravity II,10.4171/JNCG/30,Journal of Noncommutative Geometry,Johannes Aastrup,Jesper Møller Grimstrup,Ryszard Nest
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On spectral triples in quantum gravity II
(
Citations: 10
)
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Johannes Aastrup
,
Jesper Møller Grimstrup
,
Ryszard Nest
Journal:
Journal of Noncommutative Geometry
, pp. 4781, 2009
DOI:
10.4171/JNCG/30
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www.emsph.org
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Citation Context
(3)
...Its existence  as a mathematical entity  was established in [
4
,5]...
...In this section we outline the construction of the semifinite spectral triple first presented in [3,
4
] and further developed in [5]...
...This requirement is easily satisfied for the algebras and the Hilbert spaces, see [
4
]...
...tr(1) = 1. Let Tr be the ordinary operator trace on the operators on lim L 2 (G n(�) , Ml ) and define τ = Tr × tr .I n [
4
] we prove that for a compact Liegroup G the triple (B,H, D) is a semifinite spectral triple with respect to τ when the sequence {an} converges to infinity...
...In [
4
] we prove that A is densely embedded in A:...
Johannes Aastrup
,
et al.
On SemiClassical States of Quantum Gravity and Noncommutative Geometry
...The second paper [
22
] deals with the concise mathematical construction...
...However, one can show [
22
] that for a suitable choice of embedded graphs...
...This approach, which may be intuitively clearer, is applied in [
22
]...
...Let us finally remind the reader that the focus of this paper is the physical significance of the spectral triple B , D , H . The detailed mathematical analysis of the triple is given in [
22
]...
...In [
22
] we provide certain necessary requirements for a system of graphs to be suitable for the construction of a spectral triple...
Johannes Aastrup
,
et al.
On spectral triples in quantum gravity: I
...The construction is canonically associated to quantum gravity and is an alternative version of the spectral triple presented in [
1
]...
...Using this line of reasoning we successfully constructed a semifinite spectral triple over a space of connections [
1
,2]...
...In this paper we construct a new semifinite spectral triple which differs from the triple constructed in [
1
,2] through the form of the Dirac type operator...
...We recall from [
1
] how we constructed the completion of spaces of connections...
...We start with a systemS of graphs on M. The system has to be dense and directed according to the Definitions 2.1.6 and 2.1.7 in [
1
]...
...We therefore get a map from A to A S . This map is a dense embedding, see [
1
]f or...
...Like in [
1
] we define the coordinate transformation...
...For U (1) this is trivial, and the computation in the Appendix of [
1
] shows that this is also the case for SU(2), which is the example of most interest...
...The spectral triple constructed by means of the reparameterization in this article differs from the one constructed in [
1
]...
...The spectral analysis of the one constructed in [
1
] appears to be more complicated than the reparameterized ones...
Johannes Aastrup
,
et al.
A New Spectral Triple over a Space of Connections
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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
On Type II noncommutative geometry and the JLO character
(
Citations: 2
)
Alan Lai
Published in 2010.
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.
The JLO Character for The Noncommutative Space of Connections of AastrupGrimstrupNest
Alan Lai
Published in 2010.