2019 **Abstract:** We discuss the geometric characterization of the trajectory of a moving charged particle, for the case of a homogeneous electromagnetic field, in Minkowski space
double-struckE24 when 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 t…

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“…We have introduced here a new equation (Definition 3) which defines uniform quasi acceleration in a Heisenberg spacetime. This improves the results of previous works, 33–39 which handle only optical motion. In Section 3, we have the UQCM of moving charged velocity magnetic biharmonic particle in Heisenberg space background.…”

confidence: 80%

“…We have introduced here a new equation (Definition 3) which defines uniform quasi acceleration in a Heisenberg spacetime. This improves the results of previous works, 33–39 which handle only optical motion. In Section 3, we have the UQCM of moving charged velocity magnetic biharmonic particle in Heisenberg space background.…”

confidence: 80%

“…The uniform motion of the physical system, in particular, a mechanism defined along with the particle in a given appropriate spacetime structure, can be described by minimizing the action functional and can further computation be obtained by the principle of the least action [33][34][35]. The investigation of the uniform motion of the particle is very efficient for the exact comprehension of many physical processes such as vortex filaments, integrable systems, dynamics of Heisenberg chain, soliton equation theory, relativity, sigma models, water wave theory, field theories, fluid dynamics, linear and nonlinear optics, and so on.…”

confidence: 99%

“…Also, the extended direct algebraic method is used to find new soliton solutions of the fractional (4.1) equations in de Sitter space. Many partial differential equations are proceeding in mathematical physics and engineering modeling applications [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46].…”

confidence: 99%