自旋二分之一场的旋量
Spinors of Spin-one-half Fields
摘要：
本文综述了一个两态、自旋为1/2的系统在转动下的转变。然后，它使用这些知识来解释动量为零，自旋为一半的湮灭和创造算子如何在旋转下变换。然后，本文解释了如何自旋一个半场下的旋转变换。动量零旋量是从自旋半系统在旋转下的变换方式和狄拉克方程中找到的。一旦知道了零动量旋量，狄拉克方程立即给出了有限动量的旋量。然后，该文件表明，这些旋量，狄拉克场变换适当的电荷共轭，宇称和时间反转。本文还描述了如何狄拉克场可以分解成两个四分量马约拉纳场或一个二分量左手场和一个二分量右手场。维格纳旋转和温伯格推导旋量的性质也进行了讨论。
英文摘要：
This paper reviews how a two-state, spin-one-half system transforms under rotations. It then uses that knowledge to explain how momentum-zero, spin-one-half annihilation and creation operators transform under rotations. The paper then explains how a spin-one-half field transforms under rotations. The momentum-zero spinors are found from the way spin-one-half systems transform under rotations and from the Dirac equation. Once the momentum-zero spinors are known, the Dirac equation immediately yields the spinors at finite momentum. The paper then shows that with these spinors, a Dirac field transforms appropriately under charge conjugation, parity, and time reversal. The paper also describes how a Dirac field may be decomposed either into two 4-component Majorana fields or into a 2-component left-handed field and a 2-component right-handed field. Wigner rotations and Weinberg's derivation of the properties of spinors are also discussed.
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。
