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.
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Johannes Aastrup, Jesper Møller Grimstrup, Ryszard Nest, On spectral triples in quantum gravity II. J. Noncommut. Geom. 3 (2009), no. 1, pp. 47–81DOI 10.4171/JNCG/30