Bertozzini, Paolo; Conti, Roberto; Lewkeeratiyutkul, Wicharn Modular theory, non-commutative geometry and quantum gravity. (English) Zbl 1221.46068 SIGMA, Symmetry Integrability Geom. Methods Appl. 6, Paper 067, 47 p. (2010). Summary: 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’s 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 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. Cited in 7 Documents MSC: 46L87 Noncommutative differential geometry 18F99 Categories in geometry and topology 58B34 Noncommutative geometry (à la Connes) 81R60 Noncommutative geometry in quantum theory 81T05 Axiomatic quantum field theory; operator algebras 83C65 Methods of noncommutative geometry in general relativity 46L60 Applications of selfadjoint operator algebras to physics Keywords:modular theory; noncommutative geometry; spectral triple; category theory; quantum physics; space-time PDFBibTeX XMLCite \textit{P. Bertozzini} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 6, Paper 067, 47 p. (2010; Zbl 1221.46068) Full Text: DOI arXiv EuDML