  In this letter the Chern-Simons field theories are studied in the Coulomb
gauge using the Dirac's canonical formalism for constrained systems. As a
strategy, we first work out the constraints and then quantize, replacing the
Dirac brackets with quantum commutators. We find that the Chern-Simons field
theories become two dimensional models with no propagation along the time
direction. Moreover, we prove that, despite of the presence of non-trivial
self-interactions in the gauge fixed functional, the commutation relations
between the fields are trivial at any order in perturbation theory in the
absence of couplings with matter fields. If these couplings are present,
instead, the commutation relations become rather involved, but it is still
possible to study their main properties and to show that they vanish at the
tree level.
