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Symmetry, Integrability and Geometry: Methods and Applications, 2010, Volume 6, 067, 47 pp.
DOI: https://doi.org/10.3842/SIGMA.2010.067 (Mi sigma524) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Modular Theory, Non-Commutative Geometry and Quantum Gravity

Paolo Bertozzinia, Roberto Contib, Wicharn Lewkeeratiyutkulc

a Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathumthani 12121, Thailand
b Dipartimento di Scienze, Università di Chieti-Pescara "G. D’Annunzio", Viale Pindaro 42, I-65127 Pescara, Italy
c Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
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DOI: https://doi.org/10.3842/SIGMA.2010.067
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.
Keywords: modular theory; non-commutative geometry; spectral triple; category theory; quantum physics; space-time.
Received: March 30, 2010; in final form July 26, 2010; Published online August 19, 2010
Bibliographic databases:
Document Type: Article
MSC: 46L87; 46L51; 46L10; 46M15; 18F99; 58B34; 81R60; 81T05; 83C65} \tableofcontents \renewcommand{\thefootnote}{\arabic{footnote}} \setcounter{footnote}{0
Language: English
Citation: Paolo Bertozzini, Roberto Conti, Wicharn Lewkeeratiyutkul, “Modular Theory, Non-Commutative Geometry and Quantum Gravity”, SIGMA, 6 (2010), 067, 47 pp.
Citation in format AMSBIB
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\by Paolo Bertozzini, Roberto Conti, Wicharn Lewkeeratiyutkul
\paper Modular Theory, Non-Commutative Geometry and Quantum Gravity
\jour SIGMA
\yr 2010
\vol 6
\papernumber 067
\totalpages 47
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    • This publication is cited in the following 14 articles:
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