Analyticity of the scattering amplitude, causality, and high-energy bounds in quantum field theory on noncommutative space-time

In the framework of quantum field theory on noncommutative space-time with the symmetry group O(1,1)xSO(2), we prove that the Jost-Lehmann-Dyson representation, based on the causality condition taken in connection with this symmetry, leads to the mere impossibility of drawing any conclusion on the analyticity of the 2 -> 2-scattering amplitude in cos Theta, Theta being the scattering angle. Discussions on the possible ways of obtaining high-energy bounds analogous to the Froissart-Martin bound on the total cross section are also presented. (c) 2006 American Institute of Physics.