2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/200482Field theories on deformed spaces suffer from the IR/UV mxing and renormalization is generically spoiled. In work with R. Wulkenhaar, one of us realized a way to cure this desease by adding one more marginal operator. We review these ideas, show the application to $ϕ^3$ models and use heat kernel expansion methods for a scalar field theory coupled to an external gauge field on a $θ$-deformed space and derive noncommutative gauge actions.20 pages; to appear in the proceedings of the 21st Nishinomiya-Yukawa Memorial Symposium Noncommutative geometry and quantum spacetime in physics, Nishinomiya and Kyoto (Japan), 2006High Energy Physics - Theorytext