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Separation of variables in Hamilton–Jacobi equation for a charged test particle in the Stackel spaces of type (2.1)
International Journal of Geometric Methods in Modern Physics ( IF 2.1 ) Pub Date : 2020-08-31 , DOI: 10.1142/s0219887820501868
Valeriy Obukhov 1, 2
Affiliation  

We can find all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of variables in the Hamilton–Jacobi equation. Separation is carried out using the complete sets of mutually-commuting integrals of motion of type (2.1), whereby in a privileged coordinate system the Hamilton–Jacobi equation turns into a parabolic type equation.

中文翻译:

类型 (2.1) 的 Stackel 空间中带电测试粒子的 Hamilton-Jacobi 方程中的变量分离

我们可以找到 Stackel 空间的电磁势和时空度量的所有等价类,前提是经典带电测试粒子的运动方程通过 Hamilton-Jacobi 方程中的变量完全分离的方法进行积分。使用类型 (2.1) 的完整的相互对易运动积分集进行分离,由此在特权坐标系中,Hamilton-Jacobi 方程变为抛物型方程。
更新日期:2020-08-31
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