Noncommutative fermionic field theories with smooth commutative limit - art. no. 047701

We consider two model held theories on a noncommutative plane that have a s mooth commutative limit. One is the nonrelativistic single-component fermio n theory with a quartic interaction that vanishes identically in the commut ative 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 s mooth commutative limits by computing the bound state energies and the two particle scattering amplitudes exactly.