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General Relativity and Quantum Cosmology

arXiv:1007.4094 (gr-qc)
[Submitted on 23 Jul 2010 (v1), last revised 19 Aug 2010 (this version, v2)]

Title:Modular Theory, Non-Commutative Geometry and Quantum Gravity

Authors:Paolo Bertozzini, Roberto Conti, Wicharn Lewkeeratiyutkul
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Abstract:This paper contains the first written exposition of some ideas (announced in a previous survey) on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of spectral geometries from an operational formalism of states and categories of observables in a covariant theory. Care has been taken to provide a coverage of the relevant background on modular theory, its applications in non-commutative geometry and physics and to the detailed discussion of the main foundational issues raised by the proposal.
Comments: Special Issue "Noncommutative Spaces and Fields"
Subjects: General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph); Operator Algebras (math.OA); Quantum Physics (quant-ph)
MSC classes: 46L87, 46L51, 46L10, 46M15, 58B34, 18F99, 81R60, 81T05, 83C65
Cite as: arXiv:1007.4094 [gr-qc]
  (or arXiv:1007.4094v2 [gr-qc] for this version)
  https://doi.org/10.48550/arXiv.1007.4094
Journal reference: SIGMA 6:067,2010
Related DOI: https://doi.org/10.3842/SIGMA.2010.067

Submission history

From: Paolo Bertozzini [view email] [via SIGMA proxy]
[v1] Fri, 23 Jul 2010 10:17:55 UTC (67 KB)
[v2] Thu, 19 Aug 2010 05:26:57 UTC (69 KB)
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