Connes duality in Lorentzian geometry

Abstract

The Connes formula giving the dual description for the distance between points of a Riemannian manifold is extended to the Lorentzian case. It resulted that its validity essentially depends on the global structure of spacetime. The duality principle classifying spacetimes is introduced. The algebraic account of the theory is suggested as a framework for quantization along the lines proposed by Connes. The physical interpretation of the obtained results is discussed.

11 pages, latex

References in corpus (2)

• An Introduction to Noncommutative Spaces and their Geometry
• Supersymmetric quantum theory and (non-commutative) differential geometry

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