Towards Noncommutative Quantization of Gravity

Abstract

We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid constructed on space-time rather than space-time itself. Both space and time emerge in the transition process to the commutative case. Our approach clearly suggests that quantum gravitational observables should be looked for among correlations of distant phenomena rather than among local effects. A toy model is computed (based on a finite group) which predicts the value of "cosmological constants" (in the quantum sector) which vanish when going to the standard space-time physics.

25 pages, latex, no figures

References in corpus (1)

• Towards Noncommutative Quantization of Gravity

Cited by in corpus (15)

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• Noncommutative Unification of General Relativity and Quantum Mechanics
• Origin of Classical Singularities
• Path Integral Quantisation of Finite Noncommutative Geometries
• Conceptual Unification of Gravity and Quanta
• Noncommutative Unification of General Relativity and Quantum Mechanics. A Finite Model
• Observables in a Noncommutative Unification of Quanta and Gravity. A Final Model
• State Vector Reduction as a Shadow of a Noncommutative Dynamics
• Complex degenerate metrics in general relativity: a covariant extension of the Moore-Penrose algorithm
• Einstein-Podolski-Rosen Experiment from Noncommutative Quantum Gravity
• Geometry and General Relativity in the Groupoid Model with a Finite Structure Group
• Creation of Matter in a Noncommutative Universe
• Noncommutative regime of fundamental physics