电磁场中相对论电子自旋的动力学
Dynamics of the relativistic electron spin in an electromagnetic field
摘要：
相对论性自旋算符在相对论性量子力学中不能被唯一地定义。在此之前，已经提出了不同的真相对论自旋算符，例如Foldy-Wouthuysen和Pryce类型的自旋算符，它们都与自由粒子狄拉克哈密顿量交换，并表示运动常数。在这里，我们考虑相对论性电子自旋在外部电磁场的动力学。我们使用两种不同的哈密顿量来推导相应的自旋动力学。这两个是：（a）狄拉克哈密顿在存在一个外部的领域，（b）半相对论展开相同的。考虑到Foldy-Wouthuysen和Pryce自旋算子，我们表明，这些导致不同的自旋动力学在外部电磁场，这提供了可能性，以区分他们的行动。我们发现这两种自旋算符的动力学都包含自旋相关项和自旋无关项，然而，Foldy-Wouthuysen自旋动力学还考虑了相对论性的粒子-反粒子耦合.我们的结论是，Pryce自旋算子提供了一个合适的描述相对论自旋动力学在一个弱到中间的外场，而Foldy-Wouthuysen自旋算子是更适合在强场制度。
英文摘要：
A relativistic spin operator cannot be uniquely defined within relativistic quantum mechanics. Previously, different proper relativistic spin operators have been proposed, such as spin operators of the Foldy-Wouthuysen and Pryce type, that both commute with the free-particle Dirac Hamiltonian and represent constants of motion. Here we consider the dynamics of a relativistic electron spin in an external electromagnetic field. We use two different Hamiltonians to derive the corresponding spin dynamics. These two are: (a) the Dirac Hamiltonian in presence of an external field, (b) the semirelativistic expansion of the same. Considering the Foldy-Wouthuysen and Pryce spin operators we show that these lead to different spin dynamics in an external electromagnetic field, which offers possibilities to distinguish their action. We find that the dynamics of both spin operators involve spin-dependent and spin-independent terms, however, the Foldy-Wouthuysen spin dynamics additionally accounts for the relativistic particle-antiparticle coupling. We conclude that the Pryce spin operator provides a suitable description of the relativistic spin dynamics in a weak-to-intermediate external field, whereas the Foldy-Wouthuysen spin operator is more suitable in the strong field regime.
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