泡利和$\text{Lévy-Leblond}$方程以及自旋电流密度
The Pauli and $\text{Lévy-Leblond}$ Equations, and the Spin Current Density
摘要：
我们回顾了文献中的泡利方程和它的电流密度，讨论了进展从原来的唯象版本的泡利，其推导$\text{Lévy-Leblond}$从线性化的$\text{Schrödinger}$方程。$\text{Lévy-Leblond}$的研究结论是，自旋为1/2的粒子（如电子）的自旋在本质上是非相对论性的，这与狄拉克推导相对论性波动方程以及他随后证明泡利的自旋相互作用项出现在非相对论性极限中的情况相反。在这个极限下，发现相关概率流密度的戈登分解包含自旋依赖项。这样一个长期不遵循，但是，从通常的推导电流密度从泡利方程，虽然各种物理动机，但其他特设的解释提出了占it. We评论的唯一例外，这些我们都知道暗示的自旋项在当前实际上是非相对论性的。然而，$\text{Lévy-Leblond}$的早期工作已经表明，在没有附加假设的情况下，这一项是从他的方程导出的电流密度的一个突出特征。因此，就像自旋本身一样，自旋流是非相对论性的，尽管有人声称相反。我们提出了一个有点简化的推导的$\text{Lévy-Leblond}$方程和它的电流密度，评论的可能性实验工作，可能表明可测量的后果的自旋项在电流密度。
英文摘要：
We review the literature on the Pauli equation and its current density, discussing the progression from the original phenomenological version of Pauli to its derivation by $\text{Lévy-Leblond}$ from a linearization of the $\text{Schrödinger}$ equation. It was established conclusively by $\text{Lévy-Leblond}$'s work that the spin of a spin-1/2 particle such as an electron is non-relativistic in nature, contrary to what was often stated following Dirac's derivation of a relativistic wave equation, and his subsequent demonstration that Pauli's spin interaction term appeared in the non-relativistic limit. In this limit, the Gordon decomposition of the associated probability current density was found to contain a spin-dependent term. Such a term does not follow, however, from the usual derivation of the current density from the Pauli equation, although various physically motivated but otherwise ad hoc explanations were put forward to account for it. We comment on the only exception to these of which we are aware implying the spin term in the current was in fact non-relativistic in nature. However, the earlier work of $\text{Lévy-Leblond}$ had already shown, with no additional assumptions, that this term was a prominent feature of the current density derived from his equation. Hence, just as with the spin itself, the spin current was non-relativistic, claims to the contrary notwithstanding. We present a somewhat simplified derivation of the $\text{Lévy-Leblond}$ equation and its current density, commenting on possibilities for experimental work that might indicate measurable consequences of the spin term in the current density.
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