  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-A^T. 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.
