Higher Derivative Operators in the Noncommutative Schwinger Model

A study of the noncommutative Schwinger model is presented. It is shown that the Schwinger mass is not modified by the noncommutativity of spacetime till the first nontrivial order in the noncommutative parameter. Instead, a higher derivative kinetic term is dynamically generated by the lowest-order vacuum polarization diagrams. We argue that in the framework of the Seiberg-Witten map the feature of non-unitarity for a field theory with space-time noncommutativity is characterized by the presence of higher derivative kinetic terms. The $\theta$-expanded version of a unitary theory will not generate the lowest-order higher derivative quadratic terms.