Noncommutative Field Theory: Nonrelativistic Fermionic Field Coupled to   the Chern-Simons Field in 2+1 Dimensions
  We study a noncommutative nonrelativistic fermionic field theory in 2+1 dimensions coupled to the Chern-Simons field. We perform a perturbative analysis of model and show that up to one loop the ultraviolet divergences are canceled and the infrared divergences are eliminated by the noncommutative Pauli term. 
M. A. Anacleto, M. Gomes, A. J. da Silva, D. Spehler