Photon propagation in noncommutative QED with constant external field

TL;DR

This paper investigates photon behavior in noncommutative QED with external fields, revealing superluminal propagation and causality issues, while showing no birefringence at first order in noncommutativity.

Contribution

It provides the first analysis of photon dispersion laws in noncommutative QED with external fields, highlighting superluminal group velocities and causality implications.

Findings

No birefringence at first order in θ.

Photon can propagate superluminally depending on field orientation.

Causality may be violated due to superluminal group velocities.

Abstract

We find dispersion laws for the photon propagating in the presence of mutually orthogonal constant external electric and magnetic fields in the context of the $\theta $-expanded noncommutative QED. We show that there is no birefringence to the first order in the noncommutativity parameter $% \theta .$ By analyzing the group velocities of the photon eigenmodes we show that there occurs superluminal propagation for any direction. This phenomenon depends on the mutual orientation of the external electromagnetic fields and the noncommutativity vector. We argue that the propagation of signals with superluminal group velocity violates causality in spite of the fact that the noncommutative theory is not Lorentz-invariant and speculate about possible workarounds.