The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Journal of Noncommutative Geometry

Full-Text PDF (288 KB) | Metadata | Table of Contents | JNCG summary
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