On the noncommutative fields method in the three-dimensional Yang-Mills   theory
  We apply the noncommutative fields method to the three-dimensional non-Abelian gauge theory. We find that, first, implementing the noncommutativity between the canonical momenta implies in generation of the non-Abelian Chern-Simons term, second, if one introduces the noncommutativity between the field operators, the higher derivative terms would arise. 
J. R. Nascimento, A. Yu. Petrov, E. O. Silva