On semi-classical states of quantum gravity and noncommutative geometry

TY - JOUR

T1 - On semi-classical states of quantum gravity and noncommutative geometry

AU - Aastrup, Johannes

AU - Grimstrup, Jesper Møller

AU - Paschke, Mario

AU - Nest, Ryszard

PY - 2011/3

Y1 - 2011/3

N2 - 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.

AB - 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.

M3 - Journal article

SN - 0010-3616

VL - 302

SP - 675

EP - 696

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -