非交换相空间中的三维泡利方程

Ilyas Haouam
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引用次数: 9

摘要

本文得到了非交换相空间中电磁场存在下自旋1/2粒子的三维泡利方程,以及相应的形变连续性方程,其中考虑了恒定磁场和非恒定磁场的情况。由于变形连续方程中电流磁化项的缺失,我们不得不在不修改连续方程的情况下,从非对易泡利方程中提取电流磁化项。结果表明,非恒定磁场提高了泡利方程和相应的连续性方程的非交换性参数的阶数。然而,我们成功地测试了非交换性对电流密度和磁化电流的影响。利用经典处理方法,导出了单粒子和n粒子三维泡利系统的半经典非交换配分函数。然后,我们用它来计算相应的亥姆霍兹自由能,然后计算电子在交换和非交换相空间中的磁化率和磁化率。了解了三维Bopp-Shift变换和Moyal-Weyl积,我们在问题中引入了相空间非交换性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
ON THE THREE-DIMENSIONAL PAULI EQUATION IN NONCOMMUTATIVE PHASE-SPACE
In this paper, we obtained the three-dimensional Pauli equation for a spin-1/2 particle in the presence of an electromagnetic field in noncommutative phase-space, as well the corresponding deformed continuity equation, where the cases of a constant and non-constant magnetic field are considered. Due to the absence of the current magnetization term in the deformed continuity equation as expected, we had to extract it from the noncommutative Pauli equation itself without modifying the continuity equation. It is shown that the non-constant magnetic field lifts the order of the noncommutativity parameter in both the Pauli equation and the corresponding continuity equation. However, we successfully examined the effect of the noncommutativity on the current density and the magnetization current. By using a classical treatment, we derived the semi-classical noncommutative partition function of the three-dimensional Pauli system of the one-particle and N-particle systems. Then, we employed it for calculating the corresponding Helmholtz free energy followed by the magnetization and the magnetic susceptibility of electrons in both commutative and noncommutative phase-spaces. Knowing that with both the three-dimensional Bopp-Shift transformation and the Moyal-Weyl product, we introduced the phase-space noncommutativity in the problems in question.
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