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.

References in corpus (5)

• Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
• Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups
• Holonomy Loops, Spectral Triples & Quantum Gravity
• On a Derivation of the Dirac Hamiltonian From a Construction of Quantum Gravity
• The JLO Character for The Noncommutative Space of Connections of Aastrup-Grimstrup-Nest

Cited by in corpus (1)

• Lorentzian Connes Distance, Spectral Graph Distance and Loop Gravity