Intersecting Quantum Gravity with Noncommutative Geometry { a Review ?

  title={Intersecting Quantum Gravity with Noncommutative Geometry \{ a Review ?},
  author={Johannes Aastrup and Jesper M{\o}ller Grimstrup},
  journal={Symmetry Integrability and Geometry-methods and Applications},
We review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural non- commutative structures which have, hitherto, not been explored. Next, we present the con- struction 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… 

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