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 ${\theta }^{\mu \nu }$ 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 non-covariant transformation properties of the phase factors appearing in TOPT.