Dispersion relations in the noncommutative ϕ^3 and Wess-Zumino model in the Yang-Feldman formalism

Abstract

We study dispersion relations in the noncommutative ϕ^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.

arXiv comment23 pages, 2 figures. v2: Minor corrections and changes in the presentation

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• Noncommutative (supersymmetric) electrodynamics in the Yang-Feldman formalism
• Noncommutative Time in Quantum Field Theory
• Ultraviolet-infrared mixing on the noncommutative Minkowski space in the Yang-Feldman formalism
• The wave front set of oscillatory integrals with inhomogeneous phase function