Signals for noncommutative interactions at linear colliders

Recent theoretical results have demonstrated that noncommutative geometries naturally appear within the context of string or M theory. One consequence of this possibility is that QED takes on a non-Abelian nature due to the introduction of 3- and 4-point functions. In addition, each QED vertex acquires a momentum dependent phase factor. We parametrize the effects of noncommutative space-time coordinates and show that they lead to observable signatures in several $\stackrel{\ensuremath{\rightarrow}}{2}2$ QED processes in ${e}^{+}{e}^{\ensuremath{-}}$ collisions. In particular, we examine pair annihilation, Moller and Bhabha scattering, as well as $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}}\ensuremath{\gamma}\ensuremath{\gamma}$ scattering and show that noncommutative scales of order a TeV can be probed at high energy linear colliders.