https://doi.org/10.1140/epjc/s10052-025-14970-9
Regular Article - Theoretical Physics
Light propagation in 
-Minkowski space-time: gauge ambiguities and invariance
1
Dipartimento di Fisica “E. Pancini”, Università di Napoli Federico II, Complesso Universitario di Monte S. Angelo Edificio 6, Via Cintia, 80126, Napoli, Italy
2
INFN-Sezione di Napoli, Complesso Universitario di Monte S. Angelo Edificio 6, Via Cintia, 80126, Napoli, Italy
Received:
20
August
2025
Accepted:
21
October
2025
Published online:
31
October
2025
We study the noncommutative U(1) gauge theory on the -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.
© The Author(s) 2025
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