2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/183876We study properties of the zero and near-zero eigenmodes of the overlap Dirac operator in compact U(1) gauge theory. In the confinement phase the exact zero-modes are localized as found by studying the values of the inverse participation ratio and other features. Non-zero-eigenmodes are less localized in the confinement phase. In the Coulomb phase no zero-modes are observed and the eigenmodes show no localization at all.Minor corrections, 15 pages, 5 figures, LaTeX styleHigh Energy Physics - Latticetext