存在外部场的自旋 3/2 粒子的保利-菲尔兹理论中的非相对论近似值

A. Ivashkevich, V. Red'kov, A. M. Ishkhanyan
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引用次数: 0

摘要

在本文中,我们研究了笛卡尔坐标相对论方程组中 16 分量波函数的非相对论近似,该波函数在洛伦兹群下具有矢量双分量的变换特性。在进行非相对论近似时,为了分离完整波函数中的大分量和小分量,我们采用了投影算子方法。因此,完整波函数被表述为三个部分之和:大的部分取决于 6 个变量,小的部分取决于 14 个变量。我们发现大的部分有两个线性约束,小的部分有两个约束。在进行非相对论近似后,我们得出了 6 个具有必要非相对论结构的方程,其中只包括 4 个大分量。事实证明,只有 4 个方程是独立的,因此我们得出了 4 分量波函数的广义保利方程。通过分析非相对论波函数的变换特性,我们可以将导出方程的结构推广到任意弯曲的 3 空间。
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Non-relativistic approximation in the Pauli–Fierz theory for a spin 3/2 particle in the presence of external fields
In the paper, we examine the non-relativistic approximation in the relativistic system of equations in Cartesian coordinates for 16-component wave functions with transformation properties of the vector-bispinor under the Lorentz group. When performing the non-relativistic approximation, for separating large and small components in the complete wave function we apply the method of projective operators. Accordingly, the complete wave function is presented as a sum of three parts: the large part depends on 6 variables, and the small ones depend on 14 variables. We have found two linear constraints on large components and two constraints on the small ones. After performing the procedure of the non-relativistic approximation we have derived 6 equations with a needed non-relativistic structure, which include only 4 large components. It is proved that only 4 equations are independent, so we have arrived at the generalized Pauli-like equation for the 4-component wave function. The analysis of transformation properties of the non-relativistic wave function permits us to generalize the structure of the derived equation to an arbitrary curved 3-space.
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