Intersecting Quantum Gravity with Noncommutative Geometry - a Review

Details Intersecting Quantum Gravity with Noncommutative Geometry - a Review Intersecting Quantum Gravity with Noncommutative Geometry - a Review

2012-03-28

arxiv.org/abs/1203.6164v1

SIGMA 8 (2012), 018, 25 pages

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

10.3842/SIGMA.2012.018

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.

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