Superluminal Noncommutative Photons

TL;DR

This paper explores how noncommutative geometry modifies photon propagation in deformed QED, revealing conditions under which photons can travel faster than light without violating causality.

Contribution

It demonstrates that in a noncommutative QED setting, photon velocities can exceed the speed of light depending on the background magnetic field orientation, a novel insight into superluminal photon behavior.

Findings

Photon velocity exceeds light speed when propagating perpendicular to magnetic field

Electric field has no effect on photon propagation in this setup

Light-cone condition remains unchanged when propagating parallel to magnetic field

Abstract

With the help of the Seiberg-Witten map, one can obtain an effective action of a deformed QED from a noncommutative QED. Starting from the deformed QED, we investigate the propagation of photons in the background of electromagnetic field, up to the leading order of the noncommutativity parameter. In our setting (both the electric and magnetic fields are parallel to the coordinate axis $x^1$ and the nonvanishing component of the noncommutativity parameter is $\theta^{23}$), we find that the electric field has no effect on the propagation of photons, but the velocity of photons can be larger than the speed of light ($c=1$) when the propagating direction of photons is perpendicular to the direction of background magnetic field, while the light-cone condition does not change when the propagating direction is parallel to the background magnetic field. The causality associated with the superluminal photons is discussed briefly.