Connes' Distance of One-Dimensional Lattices: General Cases

Abstract

Connes' distance formula is applied to endow linear metric to three 1D lattices of different topology, with a generalization of lattice Dirac operator written down by Dimakis et al to contain a non-unitary link-variable. Geometric interpretation of this link-variable is lattice spacing and parallel transport.

Comments: Latex 7 pages; No figures