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arXiv · 0902.4191

Holonomy Loops, Spectral Triples & Quantum Gravity

Johannes Aastrup·Jesper M. Grimstrup·Ryszard Nest
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Abstract

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.

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Johannes Aastrup, Jesper M. Grimstrup, Ryszard Nest. 2009-02-24. Holonomy Loops, Spectral Triples & Quantum Gravity. https://doi.org/10.1088/0264-9381%2F26%2F16%2F165001

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