arXiv 1310.09052013-10-03quant-ph

相对论协变施特恩-格拉赫实验中的相对论自旋和狄拉克自旋

Relativistic Spin and Dirac Spin in relativistically covariant Stern-Gerlach Experiment

Taeseung Choi, Yeong Deok Han

摘要：

本文研究了相对论协变的Stern-Gerlach（SG）实验。利用经典的自旋偶极张量得到了任意坐标系下的相对论自旋，给出了协变的自旋偶极相互作用，以及自旋与自旋磁偶极矩之间的关系。由于两个原因，相对论自旋在成为大质量相对论粒子的适当自旋算符方面存在问题。首先，相对论性自旋三矢量算符不能满足自旋代数。第二，相对论粒子的SG实验提供了粒子静止框架和实验室框架中的两个观察者之间的悖论，其中粒子是运动的。我们已经证明，解决了在SG实验中的悖论的狄拉克自旋，这是由一个洛伦兹变换的狄拉克旋量表示协变定义。狄拉克自旋三矢量算符满足自旋代数。结果表明，在惯性系中，在只有磁场的情况下，利用SG实验可以在不需要粒子动量信息的情况下确定Dirac自旋。这表明，狄拉克粒子的约化自旋密度矩阵可以通过积分动量自由度来很好地定义。

英文摘要：

We have studied a relativistically covariant Stern-Gerlach (SG) experiment for a relativistic spin and a Dirac spin. We have obtained the relativistic spin in an arbitrary frame by using the classical spin dipole tensor, which gives the covariant spin dipole interactions, and the relation between a spin and a spin magnetic dipole moment. The relativistic spin is shown to have problems to become a proper spin operator for a massive relativistic particle because of two reasons. First, the relativistic spin three-vector operators cannot satisfy the spin algebra. Second, the SG experiment for the relativistic particle provides a paradox between two observers in the particle rest frame and the laboratory frame, in which the particle is moving. We have shown that the paradox in the SG experiment is resolved by the Dirac spin, which is covariantly defined by a Lorentz transformation in the Dirac spinor representation. The Dirac spin three-vector operators satisfy the spin algebra. It is shown that the SG experiment for the Dirac spin in the inertial frame, where there is only magnetic field, can determine the spin without the information of the momentum of the particle. This shows that the reduced spin density matrix for the Dirac particle can be well-defined by integrating out the momentum degrees of freedom.

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摘要：

英文摘要：

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