2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/189680Field theories on deformed spaces suffer from the IR/UV mixing and renormalization is generically spoiled. In work with R. Wulkenhaar, one of us realized a way to cure this disease by adding one more marginal operator. We review these ideas, show the application to $ϕ^3$ models and use the heat kernel expansion methods for a scalar field theory coupled to an external gauge field on a $θ$-deformed space and derive noncommutative gauge field actions.To appear in the proceedings of the Workshop "Noncommutative Geometry in Field and String Theory", Corfu, 2005 (Greece)High Energy Physics - Theorytext