Separation of variables in Hamilton-Jacobi equation for a charged test particle in the Stackel spaces of type (2.0)

TL;DR

This paper classifies electromagnetic potentials and metrics in Stackel spaces of type (2.0) that allow complete separation of variables in the Hamilton-Jacobi equation for charged particles, simplifying their equations of motion.

Contribution

It provides a complete classification of Stackel space metrics and electromagnetic potentials enabling separation of variables for charged particle dynamics.

Findings

All equivalence classes of potentials and metrics identified.

Separation of variables reduces Hamilton-Jacobi equation to a nonparabolic form.

Method applies to spaces with reciprocal-commuting integrals of motion of type (2.0).

Abstract

Found 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 reciprocal-commuting integrals of motion of type (2.0), whereby in a privileged coordinate system the Hamilton- Jacobi equation turns into a nonparabolic type equation.