https://doi.org/10.1140/epjc/s10052-025-13897-5
Regular Article - Theoretical Physics
Charged particle in Lie–Poisson electrodynamics
1
CMCC-Universidade Federal do ABC, 09210-580, Santo André, SP, Brazil
2
Dipartimento di Fisica “E. Pancini”, Università di Napoli Federico II, Complesso Universitario di Monte S. Angelo Edificio 6, via Cintia, 80126, Naples, Italy
3
INFN-Sezione di Napoli, Complesso Universitario di Monte S. Angelo Edificio 6, via Cintia, 80126, Naples, Italy
a
vladislav.kupriyanov@gmail.com
Received:
17
December
2024
Accepted:
2
February
2025
Published online:
12
February
2025
Lie–Poisson electrodynamics describes the semi-classical limit of non-commutative U(1) gauge theory, characterized by Lie-algebra-type non-commutativity. We focus on the mechanics of a charged point-like particle moving in a given gauge background. First, we derive explicit expressions for gauge-invariant variables representing the particle’s position. Second, we provide a detailed formulation of the classical action and the corresponding equations of motion, which recover standard relativistic dynamics in the commutative limit. We illustrate our findings by exploring the exactly solvable Kepler problem in the context of the 
-Minkowski (or the angular) non-commutativity, along with other examples.
© The Author(s) 2025
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