Noncommutative QED corrections to e^+e^-\to\gamma\gamma\gamma at linear collider energies

We compute the total cross section as well as angular and energy distributions for process $e^{+}{e}^{-}\to \gamma \gamma \gamma$ with both unpolarized and polarized beams in the framework of noncommutative quantum electrodynamics (NCQED). The calculation is performed in the center of mass of colliding electron and positron and is evaluated for energies and integrated luminosities appropriate to future linear colliders. We find that by using unpolarized beams it is possible to probe the Lorentz symmetry violating azimuthal dependence of the cross section. Furthermore, with polarized beams the left-right asymmetry of the CP violating NCQED amplitudes can be used to obtain bounds on the noncommutative scale ${\mathrm{\Lambda }}_{NC}$ which exceed 1.0 TeV.