标题： 光子自旋算符和泡利矩阵 显示英文标题

标题： Photon spin operator and Pauli matrix

摘要： 任何平面波的极化矢量都可以分解为一对相互正交的基矢量，称为极化基。 将这种分解视为从三组分矢量到相应两组分旋量的准酉变换，从而得到光子自旋的表示形式。 在单位旋量空间（称为琼斯空间）上定义的自旋算符$\hat{\boldsymbol \gamma}$仅沿波矢方向有分量，并在常用的极化基中由泡利矩阵之一表示。 它通过从在单位极化矢量空间（称为潘查拉特纳姆空间）上定义的自旋算符经过准酉变换而变形。 基于此理论，展示了自旋算符$\hat{\boldsymbol \gamma}$的笛卡尔分量彼此对易，以$\hbar$为单位的自旋角动量正好是斯托克斯矢量沿波矢方向的分量。 显示英文摘要

摘要： Any polarization vector of a plane wave can be decomposed into a pair of mutually orthogonal base vectors, known as a polarization basis. Regarding this decomposition as a quasi-unitary transformation from a three-component vector to a corresponding two-component spinor, one is led to a representation formalism for the photon spin. The spin operator $\hat{\boldsymbol \gamma}$ defined on the space of unit spinors, referred to as the Jones space, has only component along the wave vector and is represented by one of the Pauli matrices in the commonly used polarization basis. It is deformed by the quasi-unitary transformation from the spin operator that is defined on the space of unit polarization vectors, referred to as the Pancharatnam space. On the basis of this theory, it is shown that the Cartesian components of spin operator $\hat{\boldsymbol \gamma}$ are mutually commutative and the spin angular momentum in units of $\hbar$ is exactly the component of the Stokes vector along the wave vector.