Modular Theory, Non-Commutative Geometry and Quantum Gravity - Bertozzini, P.; Conti, R.; Lewkeeratiyutkul, W, (Symmetry, Integrability and Geometry: Methods and Applications, 2010)
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.