  We analyze the unitarity of a non-relativistic non-commutative scalar field
theory. We show that electric backgrounds spoil unitarity while magnetic ones
do not. Furthermore, unlike its relativistic counterparts, unitarity can not be
restored (at least at the level of one-to-one scattering amplitude) by adding
new states to the theory. This is a signal that the model cannot be embedded in
a natural way in string theory.
