Towards Noncommutative Quantization of Gravity

M. Heller , Wiesław Sasin

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.
Author M. Heller - [Vatican Observatory]
M. Heller,,
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, Wiesław Sasin (FMIS / DDG)
Wiesław Sasin,,
- Department of Differential Geometry
Journal seriesarXiv:gr-qc/9712009
Issue year1997
Keywords in EnglishGeneral Relativity and Quantum Cosmology
DOIDOI:10.1063/1.532186
URL http://arxiv.org/abs/gr-qc/9712009
Score (nominal)0
Score sourcejournalList
Publication indicators Scopus Citations = 16; WoS Citations = 17
Citation count*34 (2015-11-15)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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