Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space

TL;DR

This paper investigates dispersion relations and quantum field theories on noncommutative Minkowski space, revealing persistent infrared issues, the impact of supersymmetry, and effects on light speed, with a comparison of different theoretical frameworks.

Contribution

It provides a detailed analysis of dispersion relations in noncommutative QED, including the effects of covariant coordinates, supersymmetry, and the twist approach, highlighting unresolved infrared problems and physical implications.

Findings

Infrared divergences persist despite covariant coordinates.

Supersymmetry cancels certain divergences when covariant coordinates are adjusted.

Nonlinear effects can alter the speed of light in noncommutative electrodynamics.

Abstract

We study field theories on the noncommutative Minkowski space with noncommuting time. The focus lies on dispersion relations in quantized interacting models in the Yang-Feldman formalism. In particular, we compute the two-point correlation function of the field strength in noncommutative quantum electrodynamics to second order. At this, we take into account the covariant coordinates that allow the construction of local gauge invariant quantities (observables). It turns out that this does not remove the well-known severe infrared problem, as one might have hoped. Instead, things become worse, since nonlocal divergences appear. We also show that these cancel in a supersymmetric version of the theory if the covariant coordinates are adjusted accordingly. Furthermore, we study the phi^3 and the Wess-Zumino model and show that the distortion of the dispersion relations is moderate for parameters typical for the Higgs field. We also disuss the formulation of gauge theories on noncommutative spaces and study classical electrodynamics on the noncommutative Minkowski space using covariant coordinates. In particular, we compute the change of the speed of light due to nonlinear effects in the presence of a background field. Finally, we examine the so-called twist approach to quantum field theory on the noncommutative Minkowski space and point out some conceptual problems of this approach.