Academic
Publications
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

On spectral triples in quantum gravity II   (Citations: 10)
BibTex | RIS | RefWorks Download
Journal: Journal of Noncommutative Geometry , pp. 47-81, 2009
Cumulative Annual
View Publication
The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
    • ...Its existence - as a mathematical entity - was established in [4,5]...
    • ...In this section we outline the construction of the semi-finite 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 Lie-group G the triple (B,H, D) is a semi-finite 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 Aastrupet 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 Aastrupet 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 Aastrupet al. A New Spectral Triple over a Space of Connections

Sort by: