Noncommutative (supersymmetric) electrodynamics in the Yang-Feldman formalism

TL;DR

This paper investigates noncommutative supersymmetric quantum electrodynamics using the Yang-Feldman formalism, revealing nonlocal divergences and their cancellation in the supersymmetric extension, with implications for causality and renormalization.

Contribution

It introduces a supersymmetric generalization of noncommutative electrodynamics and demonstrates the cancellation of nonlocal divergences in this extended model.

Findings

Infrared divergences match previous modified Feynman rule results.

Nonlocal divergences from covariant coordinates are identified.

Supersymmetry cancels nonlocal divergences, leaving a momentum-dependent field strength normalization.

Abstract

We study quantum electrodynamics on the noncommutative Minkowski space in the Yang-Feldman formalism. Local observables are defined by using covariant coordinates. We compute the two-point function of the interacting field strength to second order and find the infrared divergent terms already known from computations using the so-called modified Feynman rules. It is shown that these lead to nonlocal renormalization ambiguities. Also new nonlocal divergences stemming from the covariant coordinates are found. Furthermore, we study the supersymmetric extension of the model. For this, the supersymmetric generalization of the covariant coordinates is introduced. We find that the nonlocal divergences cancel. At the one-loop level, the only effect of noncommutativity is then a momentum-depenent field strength normalization. We interpret it as an acausal effect and show that its range is independent of the noncommutativity scale.