Electromagnetic Duality Based on Axiomatic Maxwell Equations

Abstract

No positive result has been obtained on the magnetic monopoles search. This allows to consider different theoretical approaches as the proposed in this paper, developed in the framework of the Einstein General Relativity. The properties of second rank skew-symmetrical fields are the basis of electromagnetic theories. In the space-time the Hodge duality of these fields is narrowly related with the rotations in the SO(2) group. An axiomatic approach to a dual electromagnetic theory is presented. The main result of this paper is that the stress-energy tensor can be decomposed on two parts: the parallel and the perpendicular. The parallel part is easily integrated on the Lagrangian approach, while some problems appears with the perpendicular part. A solution with the parallel part alone is found, it generates a non-standard model of magnetic monopoles neutral to the electric charges.