论文标题
Pryce的旋转和坐标运算符在大规模迪拉克·费米斯理论中的作用
The role of Pryce's spin and coordinate operators in the theory of massive Dirac fermions
论文作者
论文摘要
结果表明，迪拉克理论的Pryce旋转操作员的组件是由Pauli旋转器空间所携带的代表的$ SU（2）$发电机，这些代表确定了Dirac方程的平面波解决方案的极化。这些运算符是通过Noether定理保守的，因此可以为各种极化定义新的保守极化算子。量子理论的相应的一粒子算子被得出，表明它们与任何极化的巨大狄拉克费米的等轴测发生器（包括动量依赖性的）是如何相关的。以这种方式，自然解决了分离保守的自旋和轨道角动量算子的问题。此外，研究了Pryce提出的作为质量中心坐标的运算符，表明在量化后，这实际上变成了偶极子一粒子操作员。例如，确定主单粒子运算符的数量是在动量狂热的基础上首次得出的。
It is shown that the components of Pryce's spin operator of Dirac's theory are $SU(2)$ generators of a representation carried by the space of Pauli's spinors determining the polarization of the plane wave solutions of Dirac's equation. These operators are conserved via Noether theorem such that new conserved polarization operators can be defined for various polarizations. The corresponding one-particle operators of quantum theory are derived showing how these are related to the isometry generators of the massive Dirac fermions of any polarization, including momentum-dependent ones. In this manner, the problem of separating conserved spin and orbital angular momentum operators is solved naturally. Moreover, the operator proposed by Pryce as mass-center coordinate is studied showing that after quantization this becomes in fact the dipole one-particle operator. As an example, the quantities determining the principal one-particle operators are derived for the first time in momentum-helicity basis.
