Intersecting quantum gravity with noncommutative geometry – a review

Johannes Aastrup ; Jesper Møller Grimstrup

Symmetry, integrability and geometry: methods and applications, Tome 8 (2012)

Résumé

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.

Détail

Keywords: quantum gravity, noncommutative geometry, semiclassical analysis.

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