2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185505One of the key ingredients of A. Connes' noncommutative geometry is a generalized Dirac operator which induces a metric(Connes' distance) on the state space. We generalize such a Dirac operator devised by A. Dimakis et al, whose Connes' distance recovers the linear distance on a 1D lattice, into 2D lattice. This Dirac operator being "naturally" defined has the so-called "local eigenvalue property" and induces Euclidean distance on this 2D lattice. This kind of Dirac operator can be generalized into any higher dimensional lattices.Latex 11pages, no figuresHigh Energy Physics - TheoryHigh Energy Physics - LatticeMathematical Physicstext