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.
Keywords
Cite
@article{arxiv.0907.5510,
title = {On Semi-Classical States of Quantum Gravity and Noncommutative Geometry},
author = {Johannes Aastrup and Jesper M. Grimstrup and Mario Paschke and Ryszard Nest},
journal= {arXiv preprint arXiv:0907.5510},
year = {2011}
}
Comments
31 pages, 10 figures