Noncommutative fermionic field theories with smooth commutative limit

We consider two model field theories on a noncommutative plane that have a smooth commutative limit. One is the nonrelativistic single-component fermion theory with a quartic interaction that vanishes identically in the commutative limit. The other is a scalar-fermion theory, which extends the scalar field theory with a quartic interaction by adding a fermion. We show the smooth commutative limits by computing the bound state energies and the two particle scattering amplitudes exactly.