{"title":"Charged particle in Lie–Poisson electrodynamics","authors":"B. S. Basilio, V. G. Kupriyanov, M. A. Kurkov","doi":"10.1140/epjc/s10052-025-13897-5","DOIUrl":null,"url":null,"abstract":"<div><p>Lie–Poisson electrodynamics describes the semi-classical limit of non-commutative <i>U</i>(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 <span>\\(\\lambda \\)</span>-Minkowski (or the angular) non-commutativity, along with other examples.</p></div>","PeriodicalId":788,"journal":{"name":"The European Physical Journal C","volume":"85 2","pages":""},"PeriodicalIF":4.2000,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1140/epjc/s10052-025-13897-5.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal C","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjc/s10052-025-13897-5","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, PARTICLES & FIELDS","Score":null,"Total":0}
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Abstract
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.
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Experimental Physics I: Accelerator Based High-Energy Physics
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