Distances in Finite Spaces from Noncommutative Geometry

Abstract

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.

27 pages, 2 figures

References in corpus (4)

• The quantum structure of spacetime at the Planck scale and quantum fields
• Metrics on State Spaces
• Spectral noncommutative geometry and quantization: a simple example
• Shadow of noncommutativity

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