Distances in Finite Spaces from Noncommutative Geometry
High Energy Physics - Theory
2015-06-26 v1 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Operator Algebras
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.
Cite
@article{arxiv.hep-th/9912217,
title = {Distances in Finite Spaces from Noncommutative Geometry},
author = {B. Iochum and T. Krajewski and P. Martinetti},
journal= {arXiv preprint arXiv:hep-th/9912217},
year = {2015}
}
Comments
27 pages, 2 figures