Moduli of quantum Riemannian geometries on <= 4 points

Details Moduli of quantum Riemannian geometries on <= 4 points Moduli of quantum Riemannian geometries on <= 4 points

2003-12-31

arxiv.org/abs/gr-qc/0312126v2

J.Math.Phys. 45 (2004) 4596-4627

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

34 pages ams-latex, 4 figures

Scientific paper

10.1063/1.1804231

We classify parallelizable noncommutative manifold structures on finite sets of small size in the general formalism of framed quantum manifolds and vielbeins introduced previously. The full moduli space is found for $\le 3$ points, and a restricted moduli space for 4 points. The topological part of the moduli space is found for $\le 9$ points based on the known atlas of regular graphs. We also discuss aspects of the quantum theory defined by functional integration.

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