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

TL;DR

This work analyzes noncommutative U(1) gauge theory on κ-Minkowski space-time in the semiclassical Lie-Poisson framework and derives exact traveling-wave solutions to the deformed Maxwell equations, revealing an arbitrary group velocity determined by a parameter alpha. The key finding is that different speeds and spatial separations across gauges are related by finite Poisson gauge transformations, and physical measurements remain invariant when units are scaled accordingly. The study shows that the gauge ambiguity in the speed of light can be absorbed into a redefinition of length, ensuring gauge-invariant observational outcomes, and it lays groundwork for subsequent quantization and inclusion of additional interactions. Overall, the paper demonstrates the internal consistency of gauge transformations in noncommutative electrodynamics and their impact on measurements of light propagation and distances.

Abstract

We study the noncommutative $U(1)$ gauge theory on the $κ$-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.