导引中心非完整性和陀螺规范任意性的一种内禀方法
On an intrinsic approach of the guiding-center anholonomy and gyro-gauge-arbitrariness
摘要：
在导引中心理论中，标准陀螺角坐标与陀螺-规范相关性、垂直于磁场的单位矢量的整体存在性问题以及非完整性概念（即陀螺角在绕位形空间中的一个环传输后不能返回到其原始值）相关联。我们分析这三个有趣的话题，通过最近提出的，全球性的，规范独立的陀螺角的镜头。该坐标是受约束的，因此需要使用协变导数。着重阐述了陀螺规范自由度和非完整性的内在含义和物理内容。事实上，有许多可能的协变导数与固有陀螺角相容，每种可能性对应于不同的陀螺角输运概念。这一观察揭示了新的光Littlejohn的陀螺角运输的概念，并提出了一个新的推导最近发现的全球存在条件的单位矢量垂直于磁场。我们还讨论了笛卡尔位置-动量坐标与内禀陀螺角之间的关系。
英文摘要：
In guiding center theory, the standard gyro-angle coordinate is associated with gyro-gauge dependence, the global existence problem for unit vectors perpendicular to the magnetic field, and the notion of anholonomy, which is the failure of the gyro-angle to return to its original value after being transported around a loop in configuration space. We analyse these three intriguing topics through the lens of a recently proposed, global, gauge-independent gyro-angle. This coordinate is constrained, and therefore necessitates the use of a covariant derivative. It also highlights the intrinsic meaning and physical content of gyro-gauge freedom and anholonomy. There are, in fact, many possible covariant derivatives compatible with the intrinsic gyro-angle, and each possibility corresponds to a different notion of gyro-angle transport. This observation sheds new light on Littlejohn's notion of gyro-angle transport and suggests a new derivation of the recently-discovered global existence condition for unit vectors perpendicular to the magnetic field. We also discuss the relationship between Cartesian position-momentum coordinates and the intrinsic gyro-angle.
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