Light Propagation in $\kappa$-Minkowski Space-Time: Gauge Ambiguities and Invariance

TL;DR

This paper investigates gauge ambiguities in noncommutative $U(1)$ gauge theory on $ppa$-Minkowski space-time, revealing that the apparent variability in light speed is gauge-dependent and can be absorbed into length units, thus unmeasurable.

Contribution

It provides exact solutions to deformed Maxwell equations and demonstrates gauge invariance of physical measurements despite gauge ambiguities in wave propagation speed.

Findings

Propagation velocity is arbitrary and gauge-dependent.

Wave packets with different velocities are related by gauge transformations.

Gauge ambiguities in light speed can be absorbed into length units.

Abstract

We study the noncommutative $U(1)$ gauge theory on the $\kappa$-Minkowski space-time at the semiclassical approximation. We construct exact solutions of the deformed Maxwell equations in vacuum, describing localized signals propagating in a given direction. The propagation velocity appears to be arbitrary. We figure out that the wave packets with different values of the propagation velocity are related by noncommutative gauge transformations. Moreover, we show that spatial distances between particles are gauge-dependent as well. We explain how these two gauge dependencies compensate each other, recovering gauge invariance of measurement results. According to our analysis, the gauge ambiguity of the speed of light can be absorbed into a redefinition of the unit of length and, therefore, cannot be measured experimentally.