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.

本文回顾了两态自旋半系统在旋转下如何转换。然后，它使用该知识来解释动量零动量一半自旋an灭和创造算子在旋转下如何转换。然后，论文解释了自旋半场在旋转下如何转换。动量为零的旋量是从自旋半系统在旋转下的转化方式和狄拉克方程式得出的。一旦知道零动量的旋量，狄拉克方程立即产生有限动量的旋量。然后，论文表明，利用这些自旋，在电荷共轭，奇偶校验和时间反转的情况下，狄拉克场发生了适当的变换。本文还描述了Dirac场如何分解成两个4分量的Majorana场或2分量的左手场和2分量的右手场。