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

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.