Distances on a one-dimensional lattice from noncommutative geometry

Abstract

In the following paper we continue the work of Bimonte-Lizzi-Sparano on distances on a one dimensional lattice. We succeed in proving analytically the exact formulae for such distances. We find that the distance to an even point on the lattice is the geometrical average of the ``predecessor'' and ``successor'' distances to the neighbouring odd points.

Comments: LaTeX file, few minor typos corrected, 9 pages