Journal of Noncommutative Geometry

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Volume 3, Issue 1, 2009, pp. 47–81
DOI: 10.4171/JNCG/30

Published online: 2009-03-31

On spectral triples in quantum gravity II

Johannes Aastrup[1], Jesper Møller Grimstrup[2] and Ryszard Nest[3]

(1) SFB 478 "Geometrische Strukturen in der Mathematik", Münster
(2) Niels Bohr Institute, Copenhagen
(3) University of Copenhagen

A semifinite spectral triple for an algebra canonically associated to canonical quantum gravity is constructed. The algebra is generated by based loops in a triangulation and its barycentric subdivisions. The underlying space can be seen as a gauge fixing of the unconstrained state space of Loop Quantum Gravity. This article is the second of two papers on the subject.

Keywords: Noncommutative geometry, semifinite spectral triples, spaces of connections, Dirac operators, holonomy loops, lattice gauge theory

Aastrup Johannes, Grimstrup Jesper Møller, Nest Ryszard: On spectral triples in quantum gravity II. J. Noncommut. Geom. 3 (2009), 47-81. doi: 10.4171/JNCG/30