General form of the maxwell equations and group of external transformations of electromagnetic quantities

The Maxwell equations in their general form, corresponding to the presence of electric and magnetic charge and currents, are shown to be invariant with respect to a previously unknown group, the group of external transformations of electromagnetic quantities. The introduction of this group is based essentially on the use of an algebraic method of writing the Maxwell equations in terms of a real-spinor basis algebra (one of the real forms of Clifford algebra). The algebraic notation is also used to determine the transformation properties of electromagnetic quantities with respect to spatial and temporal reflections.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 19–23, December, 1969.The author thanks A. Z. Petrov, D. D. Ivanenko, A. E. Levashov, the participants in the seminars under their guidance, and participants of the Ivanovo Interinstitute Seminar on Mathematical Physics for discussion of these results.