2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/188462We compute a Chern-Simons term induced by the fermions on noncommutative torus interacting with two U(1) gauge fields. For rational noncommutativity θ\propto P/Q we find a new mixed term in the action which involves only those fields which are (2π)/Q periodic, like the fields in a crystal with Q^2 nodes.9 pp; v2: references and discussion addedHigh Energy Physics - Theorytext