Jordan-Schwinger映射、三维谐振子运动常数以及表征电磁波极化的经典和量子参数
Jordan-Schwinger map, 3D harmonic oscillator constants of motion, and classical and quantum parameters characterizing electromagnetic wave polarization
摘要：
在这项工作中，我们介绍了一个推广的Jauch和Rohrlich量子斯托克斯算子时，从源的到达方向是未知的{ \it先验}。我们将广义Stokes算子定义为具有Gell-Mann和Ne'eman SU（3）对称群矩阵的三重谐振子的Jordan-Schwinger映射。证明了Jordan-Schwinger映射的元素是三维各向同性谐振子的运动常数。我们还证明了广义Stokes算子与Gell-Mann矩阵和Ne'eman矩阵一起可以用来展开极化密度矩阵。通过取电磁场三模相干态中Stokes算符的期望值，得到了相应的广义经典Stokes参量。最后，利用经典三维各向同性谐振子的运动常数描述了极化椭圆的几何性质
英文摘要：
In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown {\it a priori}. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman SU(3) symmetry group matrices. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that generalized Stokes Operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization density matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical three-dimensional isotropic harmonic oscillator we describe the geometric properties of the polarization ellipse
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