  We consider a scalar $\phi^4$ 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.
