1998/01/10 by Wojciech Florek, Florek, Wojciech
Engineering · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Particle Accelerators and Free-Electron Lasers #Particle accelerators and beam dynamics #Quantum Physics (quant-ph) #Superconducting Materials and Applications #cond-mat.mes-hall #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9801017
RevTeX, 5 pages, submitted to Int. J. Mod. Phys. B
openalex publication_date 1998/01/10 · arxiv created 2002/12/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the case of a constant uniform magnetic field it can be assumed, without the loss of generality, that the vector potential (the gauge) is a linear function of position, i.e. it could be considered as a three-dimensional real matrix or, more generally in an n-dimensional space, as a tensor A of the rank two. The magnetic tensor H is obtained from A by antisymmetrization, i.e. H=A-AT. It is shown that the transpose of A plays a special role, since it determines the operator of the orbit center of a charged particle moving in an external magnetic field H. Moreover, this movement can be considered as a combination of N<=n independent cyclotronic movements in orthogonal planes (cyclotron orbits) with quantized energies, whereas in other n-2N dimensions the particle is completely free with a continuous energy spectrum. The proposed approach enables introduction of the four-dimensional space-time and, after some generalizations, non-linear gauges.