Electromagnetic forces work on particles which have electric charge.
The the potential energy of a charged particle equals the charge times the scalar potential. The potential momentum of a charged particle equals the charge times the vector potential. Electric and magnetic fields are defined by rather messy formulas in terms of space and time derivatives of the scalar and vector potentials. We write the force on charged particles in terms of the electric and magnetic fields. However, since the components of the four-potential differ in different reference frames, so do the components of the electric and magnetic fields.