Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-02-24
Class.Quant.Grav.26:165001,2009
Physics
High Energy Physics
High Energy Physics - Theory
24 pages, 7 figures, based on talk given by J.M.G. at the QG2 conference, Nottingham, juli 2008; at the QSTNG conference in Ro
Scientific paper
10.1088/0264-9381/26/16/165001
We review the motivation, construction and physical interpretation of a semi-finite spectral triple obtained through a rearrangement of central elements of loop quantum gravity. The triple is based on a countable set of oriented graphs and the algebra consists of generalized holonomy loops in this set. The Dirac type operator resembles a global functional derivation operator and the interaction between the algebra of holonomy loops and the Dirac type operator reproduces the structure of a quantized Poisson bracket of general relativity. Finally we give a heuristic argument as to how a natural candidate for a quantized Hamiltonian might emerge from this spectral triple construction.
Aastrup Johannes
Grimstrup Jesper M.
Nest Ryszard
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