New derivation for the equations of motion for particles in electromagnetism

TL;DR

This paper derives new equations of motion for charged particles in electromagnetism that avoid divergences, encompass known equations like Lorentz-Dirac and Landau-Lifshitz, and extend to higher orders.

Contribution

It introduces a balanced derivation of particle equations of motion that unifies and generalizes existing models without explicit divergences.

Findings

Derivation includes Lorentz-Dirac and Landau-Lifshitz equations as special cases.

Explicit third-order equations provided for practical calculations.

Analysis reveals unique behavior at second order in interaction.

Abstract

We present equations of motion for charged particles using balanced equations, and without introducing explicitly divergent quantities. This derivation contains as particular cases some well known equations of motion, as the Lorentz-Dirac equations. An study of our main equations in terms of order of the interaction with the external field conduces us to the Landau-Lifshitz equations. We find that the analysis in second order show a special behavior. We give an explicit presentation up to third order of our main equations, and expressions for the calculation of general orders.