  We consider the model of a massless charged scalar field, in (2+1)
dimensions, with a self interaction of the form $lambda (\phi^* \phi)^3$ and
interacting with a Chern Simons field. We calculate the renormalization group
$\beta$ functions of the coupling constants and the anomalous dimensions
$\gamma$ of the basic fields. We show that the interaction with the Chern
Simons field implies in a $\beta_{\lambda}$ which suggests that a dynamical
symmetry breakdown occurs. We also study the effect of the Chern Simons field
on the anomalous dimensions of the composite operators $(\phi^* \phi)^n$,
getting the result that their operator dimensions are lowered.
