Mondal Ritwik, Oppeneer Peter M
Fachbereich Physik and Zukunftskolleg, Universität Konstanz, DE-78457 Konstanz, Germany.
Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden.
J Phys Condens Matter. 2020 Aug 17;32(45). doi: 10.1088/1361-648X/aba675.
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 the presence of an external field, and (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.
在相对论量子力学中，相对论性自旋算符无法唯一确定。此前，人们提出了不同的合适的相对论性自旋算符，比如福尔德 - 伍斯胡森型和普赖斯型的自旋算符，它们都与自由粒子狄拉克哈密顿量对易，且代表运动常数。在此，我们考虑相对论性电子自旋在外部电磁场中的动力学。我们使用两个不同的哈密顿量来推导相应的自旋动力学。这两个哈密顿量分别是：(a) 存在外部场时的狄拉克哈密顿量，以及 (b) 其半相对论展开式。考虑福尔德 - 伍斯胡森和普赖斯自旋算符，我们表明它们在外部电磁场中会导致不同的自旋动力学，这为区分它们的作用提供了可能。我们发现，两个自旋算符的动力学都涉及自旋相关项和自旋无关项，然而，福尔德 - 伍斯胡森自旋动力学还额外考虑了相对论性粒子 - 反粒子耦合。我们得出结论，普赖斯自旋算符为弱到中等强度外部场中的相对论性自旋动力学提供了合适的描述，而福尔德 - 伍斯胡森自旋算符在强场区域更适用。
