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We consider non-Lorentzian expansions, Galilean and Carrollian, of theLorentz force equation in which both the particle position and theelectro-magnetic field are expanded. There are two well-known limits in thecase of a constant field, called electric and magnetic, that are studiedseparately. We show that the resulting equations of motion follow equivalentlyfrom considering a non-linear realisation of a certain infinite-dimensionalalgebras.

Non-Lorentzian expansions of the Lorentz force and kinematical algebras