2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/190650Non-singular instantons are shown to exist on noncommutative R^4 even with a U(1) gauge group. Their existence is primarily due to the noncommutativity of the space. The relation between U(1) instantons on noncommutative R^4 and the projection operators acting on the representation space of the noncommutative coordinates is reviewed. The integer number of instantons on the noncommutative R^4 can be understood as the winding number of the U(1) gauge field as well as the dimension of the projection on the representation space.49 pages, 7 figures, based on talk given at APCTP-Yonsei Workshop on Noncommutative Field TheoriesHigh Energy Physics - Theorytext