Separation of variables in Hamilton-Jacobi equation for a charged test particle in the Stackel spaces of type (2.1)

TL;DR

This paper classifies electromagnetic potentials and metrics in Stackel spaces of type (2.1) that allow complete separation of variables in the Hamilton-Jacobi equation for charged particles, simplifying their equations of motion.

Contribution

It provides a comprehensive classification of Stackel space configurations enabling complete separation of variables for charged particle dynamics.

Findings

All equivalence classes of potentials and metrics identified.

Separation reduces Hamilton-Jacobi equation to a parabolic form.

Method applies to classical charged test particles in Stackel spaces.

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 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.