Intersecting Quantum Gravity with Noncommutative Geometry  a Review
Abstract
We review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural noncommutative structures which have, hitherto, not been explored. Next, we present the construction of a spectral triple over an algebra of holonomy loops. The spectral triple, which encodes the kinematics of quantum gravity, gives rise to a natural class of semiclassical states which entail emerging fermionic degrees of freedom. In the particular semiclassical approximation where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges. We end the paper with an extended outlook section.
 Publication:

SIGMA
 Pub Date:
 March 2012
 DOI:
 10.3842/SIGMA.2012.018
 arXiv:
 arXiv:1203.6164
 Bibcode:
 2012SIGMA...8..018A
 Keywords:

 quantum gravity; noncommutative geometry; semiclassical analysis;;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 SIGMA 8 (2012), 018, 25 pages