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) [1] 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 [2] 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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References[edit | edit source]
- ↑ Cite error: Invalid
<ref>tag; no text was provided for refs namedAC94,CA85 - ↑ 2.0 2.1 Abhay Ashtekar and Jerzy Lewandowski. 2005. Quantum Geometry and Its Applications. Available PDF download.
- ↑ A. Connes. 1994. Noncommutative Geometry . Academic Press: New York and London.
- ↑ Connes, A. 1985 .Non-commutative differential geometry I--II. Publication Math\'ematiques IHES , {\mathbf 62}, 41--144.