On Semi-Classical States of Quantum Gravity and Noncommutative Geometry

Abstract

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.

31 pages, 10 figures

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• On a Derivation of the Dirac Hamiltonian From a Construction of Quantum Gravity
• Lattice Loop Quantum Gravity
• On a Lattice-Independent Formulation of Quantum Holonomy Theory
• The JLO Character for The Noncommutative Space of Connections of Aastrup-Grimstrup-Nest