任何线性规范的带电粒子轨道中心
Center of the charged particle orbit for any linear gauge
摘要：
在恒定均匀磁场的情况下，可以假设，不失一般性，矢势（规范）是位置的线性函数，即它可以被认为是三维实矩阵，或者更一般地在n维空间中，作为秩为2的张量A。磁张量H由A通过反对称化得到，即H=A-A^T。结果表明，A的转置起着特殊的作用，因为它决定了带电粒子在外磁场H中运动的轨道中心的算符。此外，这种运动可以被认为是在正交平面（回旋轨道）中N<=n个独立的回旋运动与量子化能量的组合，而在其他n-2N维中，粒子是完全自由的，具有连续的能谱。所提出的方法，使四维时空的介绍，经过一些推广，非线性仪表。
英文摘要：
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.
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