Lorentz transformation of electromagnetic pulses derived from Hertz potentials

Abstract

Electric and magnetic Hertz potentials are a formalism for obtaining solutions of Maxwell's equations from solutions of the inhomogeneous wave equation, with polarisation and magnetisation as the sources. We provide an overview of their covariant transformation properties, and examine an application of Hertz potentials to the Lorentz transformation of localised pulses by Lekner, who obtained a result seeming to contradict Von Laue's theorem. We show that Lekner's result of total energy-momentum not transforming as a four-vector was due to an erroneous transformation of Hertz potentials, that did not take into account their bivector nature.