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quantum Riemannian geometry
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(Topic)
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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).
- 1
- A. Connes. 1994. Noncommutative Geometry. Academic Press: New York and London.
- 2
- Connes, A. 1985 .Non-commutative differential geometry I–II. Publication Mathématiques IHES, 62, 41–144.
- 3
- Abhay Ashtekar and Jerzy Lewandowski. 2005. Quantum Geometry and Its Applications. Available PDF download.
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"quantum Riemannian geometry" is owned by bci1.
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See Also: Einstein's GR field equations, Mikhail Gromov, developments of relativity theories, Morita equivalence lemma for arbitrary algebras, algebraic topology, non-Abelian Quantum Algebraic Topology
| Other names: |
non-commutative geometry, non-Abelian geometry, non-Abelian Topology, noncommutative topology, nonabelian algebraic topology, NAAT |
| Also defines: |
quantum gravity based on noncommutative geometry/noncommutative operator algebra, nonabelian algebraic topology, NAAT, Riemannian geometry, quantum geometry, deformed Riemannian geometry |
| Keywords: |
quantum gravity theories, non-commutative geometry, non-Abelian geometry, non-Abelian topology, noncommutative topology |
Cross-references: GR, Einstein's, manifold, spin network, string theories, QTL, quantum theories on a lattice, HQFT, homotopy, TQFT, quantum field theory, topological, AQFT, LQG, space-times, non-Abelian, operator, SUSY, noncommutative geometry, quantum gravity
There are 17 references to this object.
This is version 4 of quantum Riemannian geometry, born on 2008-10-19, modified 2009-05-09.
Object id is 317, canonical name is QuantumRiemannianGeometry.
Accessed 3258 times total.
Classification:
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Pending Errata and Addenda
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