Space-time noncommutative field theories and unitarity

We study the perturbative unitarity of noncommutative scalar held theories. Field theories with space-time noncommutativity do not have a unitary S-ma trix. Field theories with only space noncommutativity are perturbatively un itary. This can be understood from string theory, since space noncommutativ e field theories describe a low energy limit of string theory in a backgrou nd magnetic field. On the other hand, there is no regime in which space-tim e noncommutative field theory is an appropriate description of string theor y. Whenever space-time noncommutative field theory becomes relevant massive open string states cannot be neglected. (C) 2000 Elsevier Science B.V. All rights reserved.