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

TL;DR

This paper investigates how noncommutative geometry affects dispersion relations in ^3 and Wess-Zumino models, revealing moderate distortions at the Planck scale through rigorous oscillatory integral calculations.

Contribution

It provides a detailed analysis of nonplanar graph effects on dispersion relations in noncommutative quantum field theories using the Yang-Feldman formalism.

Findings

Nonplanar graphs distort dispersion relations.

Effect is moderate at Planck scale.

Rigorous calculation via oscillatory integrals.

Abstract

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.