Modular Theory, Non-Commutative Geometry and Quantum Gravity

Details Modular Theory, Non-Commutative Geometry and Quantum Gravity Modular Theory, Non-Commutative Geometry and Quantum Gravity

2010-07-23

arxiv.org/abs/1007.4094v2

SIGMA 6:067,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Special Issue "Noncommutative Spaces and Fields"

Scientific paper

10.3842/SIGMA.2010.067

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.

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