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On the uniform motion of a relativistic charged particle in a homogeneous electromagnetic field in Minkowski space E 2 4
Author(s) -
Körpinar Talat,
Demirkol Rıdvan Cem
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5567
Subject(s) - minkowski space , electromagnetic field , classical mechanics , lorentz transformation , antisymmetric tensor , physics , electromagnetic tensor , relativistic particle , charged particle , field (mathematics) , lorentz force , magnetic field , mathematics , maxwell's equations , mathematical physics , quantum mechanics , gauge theory , ion , pure mathematics , electron
We discuss the geometric characterization of the trajectory of a moving charged particle, for the case of a homogeneous electromagnetic field, in Minkowski spaceE 2 4when the motion is governed by the Lorentz equation. We employ a totally relativistic approach during the discussion. It is based on a systematic use of the Faraday antisymmetric tensor properties of the electromagnetic field and of the four‐dimensional Frenet‐Serret formula, which is adapted to the Minkowski 4‐space with index two to determine the worldline geometry of the electromagnetic field acting on the particle. Finally, we present the necessary and sufficient conditions to obtain uniform motion of the relativistic charged particle in a homogeneous electromagnetic field inE 2 4 .