Noncommutative Field Theories and Smooth Commutative Limits
  We consider two model field theories on a noncommutative plane that have smooth commutative limits. One is the single-component fermion theory with quartic interaction that vanishes identically in the commutative limit. The other is a scalar-fermion theory, which extends the scalar field theory with quartic interaction by adding a fermion. We compute the bound state energies and the two particle scattering amplitudes exactly. 
Dongsu Bak, Sung Ku Kim, Kwang-Sup Soh and Jae Hyung Yee