Distances in Finite Spaces from Noncommutative Geometry

Details Distances in Finite Spaces from Noncommutative Geometry Distances in Finite Spaces from Noncommutative Geometry

1999-12-22

arxiv.org/abs/hep-th/9912217v1

J.Geom.Phys. 37 (2001) 100-125

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, 2 figures

Scientific paper

Following the general principles of noncommutative geometry, it is possible to define a metric on the space of pure states of the noncommutative algebra generated by the coordinates. This metric generalizes the usual Riemannian one. We investigate some general properties of this metric in the finite commutative case which corresponds to a metric on a finite set, and also give some examples of computations in both commutative and noncommutative cases.

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