# On the Derivation and Interpretation of the Poincar\'e-Maxwell Group

## TL;DR

This paper derives the Lie algebra of the Poincaré-Maxwell group, clarifies its connection to charged particle dynamics in electromagnetic fields, and discusses the structure of its coadjoint orbits.

## Contribution

It provides a new derivation of the Poincaré-Maxwell Lie algebra and interprets the equations of motion via the orbit method, linking group theory to classical electromagnetism.

## Key findings

- The Lie algebra of the Poincaré-Maxwell group is explicitly derived.
- The orbit method's dynamics are shown to match classical charged particle motion.
- The structure and multiplicity of coadjoint orbits are analyzed.

## Abstract

The Lie algebra of the Poincar\'e-Maxwell group is derived in a manner that provides the interpretation of the equations of motion. It is clarified that the dynamics obtained from the orbit method is exactly equivalent to the classical description of the charged particle moving in the constant electromagnetic field. The multiplicity of the coadjoint orbits of the group under consideration is discussed.