Charged Particle in Lie-Poisson Electrodynamics

Autor:	Basilio, B. S., Kupriyanov, V. G., Kurkov, M. A.
Rok vydání:	2024
Předmět:	High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics
Druh dokumentu:	Working Paper
Popis:	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 $\lambda$-Minkowski (or the angular) non-commutativity, along with other examples. Comment: 19 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.10247 Zobrazit plný text záznamu View this record from Arxiv