2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/201503We consider a scalar $ϕ^4$ theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner to the scalar field. We extract the dynamics for the gauge field from the divergent terms of the 1-loop effective action using a matrix basis and propose an action for the noncommutative gauge theory, which is a candidate for a renormalisable model.Typos corrected, one reference added; eqn. (49) corrected, one equation number added; 30 pagesHigh Energy Physics - Theorytext