PlanetPhysics/Quantum Riemannian Geometry

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) 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 in place of the classical Riemannian manifold that is employed in the well-known, Einstein's classical approach to General Relativity (GR).