On Semi-Classical States of Quantum Gravity and Noncommutative Geometry

TL;DR

This paper constructs semi-classical states in a quantum gravity model based on spectral triples, revealing emergent classical fields and potential fermionic matter, while clarifying ambiguities in the initial formulation.

Contribution

It introduces a refined semi-classical analysis of a spectral triple-based quantum gravity model, resolving previous ambiguities and demonstrating emergent classical fields and matter.

Findings

Emergence of Dirac Hamiltonian in the semi-classical limit

Time-independent lapse and shift fields from semi-classical states

Potential fermionic matter degrees of freedom

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.