Violation of remaining Lorentz symmetry in the approach of time-ordered perturbation theory to space-time noncommutativity

We study remaining Lorentz symmetry, i.e., Lorentz transformations which leave the noncommutativity parameter θμν invariant, within the approach of time-ordered perturbation theory (TOPT) to space-time noncommutative theories. Their violation is shown in a simple scattering process. We argue that this results from the noncovariant transformation properties of the phase factors appearing in TOPT.