Modular Theory, Non-Commutative Geometry and Quantum Gravity

Symmetry Integrability and Geometry-Methods and Applications

article

Paolo Bertozzini¹  Roberto Conti²  Wicharn Lewkeeratiyutkul³ 

[1] Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University;Dipartimento di Scienze, Università di Chieti-Pescara ''G. D'Annunzio'';Department of Mathematics, Faculty of Science, Chulalongkorn University

关键词: modular theory;    non-commutative geometry;    spectral triple;    category theory;    quantum physics;    space-time;   

DOI  :  10.3842/SIGMA.2010.067

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown