Modular Theory, Non-Commutative Geometry and Quantum Gravity

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.

Special Issue "Noncommutative Spaces and Fields"

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Cited by in corpus (11)

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• Relative entropy for coherent states from Araki formula
• A modular spectral triple for $\kappa$-Minkowski space
• C*-algebras of Holonomy-Diffeomorphisms & Quantum Gravity I
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• On Strict Higher C*-categories
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