Description: Quantum geometry (or quantum geometries) is an approach (resp. are approaches) to quantum gravity based on either noncommutative geometry and SUSY (the `Standard' Model of current Physics) [1,2] or modified or `deformed' Riemannian, `quantum' geometry, with additional assumptions regarding a generalized `Dirac' operator, the `spectral triplet' with non-Abelian structures of quantized space-times.
Remarks.
Other approaches to Quantum Gravity include: Loop Quantum Gravity (LQG), AQFT
approaches,
topological
quantum field theory
(TQFT)/ homotopy
Quantum Field Theories (HQFT; Tureaev and Porter, 2005),
quantum theories on a lattice
(QTL), string theories
and spin network
models.
An interesting, but perhaps limiting approach, involves `quantum' Riemannian geometry [3] in place of the classical Riemannian manifold that is employed in the well-known, Einstein's classical approach to General Relativity (GR).
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