Dispersion relations in the noncommutative φ³ and Wess-Zumino model in the Yang-Feldman formalism

We study dispersion relations in the noncommutative \phi^3 and Wess-Zumino model in the Yang-Feldman formalism at one-loop order. Nonplanar graphs lead to a distortion of the dispersion relation. We find that the strength of this effect is moderate if the scale of noncommutativity is identified with the Planck scale and parameters typical for a Higgs field are employed. The contribution of the nonplanar graphs is calculated rigorously using the framework of oscillatory integrals.