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 finite commutative cases corresponding to a metric on a finite set, and also compute explicitly some distances associated to commutative or noncommutative algebras.
 Publication:

Journal of Geometry and Physics
 Pub Date:
 January 2001
 DOI:
 10.1016/S03930440(00)000449
 arXiv:
 arXiv:hepth/9912217
 Bibcode:
 2001JGP....37..100I
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Mathematical Physics;
 Mathematics  Operator Algebras
 EPrint:
 27 pages, 2 figures