On Semi-Classical States of Quantum Gravity and Noncommutative Geometry

Details On Semi-Classical States of Quantum Gravity and Noncommutative Geometry On Semi-Classical States of Quantum Gravity and Noncommutative Geometry

2009-07-31

arxiv.org/abs/0907.5510v1

Commun.Math.Phys.302:675-696,2011

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, 10 figures

Scientific paper

10.1007/s00220-010-1181-x

We construct normalizable, semi-classical states for the previously proposed model of quantum gravity which is formulated as a spectral triple over holonomy loops. The semi-classical limit of the spectral triple gives the Dirac Hamiltonian in 3+1 dimensions. Also, time-independent lapse and shift fields emerge from the semi-classical states. Our analysis shows that the model might contain fermionic matter degrees of freedom. The semi-classical analysis presented in this paper does away with most of the ambiguities found in the initial semi-finite spectral triple construction. The cubic lattices play the role of a coordinate system and a divergent sequence of free parameters found in the Dirac type operator is identified as a certain inverse infinitesimal volume element.

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