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The effective polarization and magnetization fields in terms of charge-current densities

In the context of electrodynamics of continuous media, the electromagnetic response of a generic medium is usually described in terms of the polarization and magnetization fields P (r, t) and M (r, t), the physical content of which is connected to the multipole expansion of the response of the medium. In this paper, the formal definition of effective polarization and magnetization fields is discussed, these fields being dealt with as potentials of a gauge transformation that is shown to be a particular case of the Serdyukov–Fedorov duality transformation. On the basis of the basic connections of the charge-current densities to the polarization-magnetization potentials, a specific and novel form for P (r, t) and M (r, t) is obtained and the gauge functions whose spatial and temporal derivatives transform such potentials into another equivalent set are determined.