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arXiv 1702.00722physics.plasm-phquant-ph
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长标度近似下自旋1/2粒子的完全相对论性动力学方程

Fully relativistic kinetic equation for spin-1/2 particles in the long scale-length approximation

Robin Ekman, Felipe A. Asenjo, Jens Zamanian

摘要:

在本文中,我们推导出一个完全相对论性的自旋1/2粒子的动力学理论及其耦合麦克斯韦方程组,有效的长尺度长度的限制,其中的字段变化的尺度远长于本地化的粒子,我们工作到一阶$\hbar$。我们的出发点是一个Foldy-Wouthuysen(FW)变换,适用于这个政权,狄拉克哈密顿。导出了外电磁场中维格纳准分布的演化方程。使用拉格朗日方法,我们发现表达式的电荷和电流密度,表示为自由和约束部分。进一步发现,速度与动量变量之间存在非平凡的关系,其差别取决于自旋和外部电磁场。这一事实之前已经被讨论为“隐藏的动量”,并且是由于FW变换将点状粒子映射到粒子云,对于这些粒子云,最小耦合的处方是不正确的,因为它们具有多极矩。我们表示能量和动量守恒的质点系和电磁场,并讨论我们的结果的背景下的亚伯拉罕-闵可夫斯基困境。

英文摘要:

In this paper we derive a fully relativistic kinetic theory for spin-1/2 particles and its coupling to Maxwell's equations, valid in the long scale-length limit, where the fields vary on a scale much longer than the localization of the particles; we work to first order in $\hbar$. Our starting point is a Foldy-Wouthuysen (FW) transformation, applicable to this regime, of the Dirac Hamiltonian. We derive the corresponding evolution equation for the Wigner quasi-distribution in an external electromagnetic field. Using a Lagrangian method we find expressions for the charge and current densities, expressed as free and bound parts. It is furthermore found that the velocity is non-trivially related to the momentum variable, with the difference depending on the spin and the external electromagnetic fields. This fact that has previously been discussed as "hidden momentum" and is due to that the FW transformation maps pointlike particles to particle clouds for which the prescription of minimal coupling is incorrect, as they have multipole moments. We express energy and momentum conservation for the system of particles and the electromagnetic field, and discuss our results in the context of the Abraham-Minkowski dilemma.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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