A repulsive interaction in the classical electrodynamics

Abstract

Herein, we introduce an additional term into the induction equation (one of the Maxwell’s equation). The related Lagrangian formalism applying the scalar and vector potentials is fitted to this modified Maxwell’s equations. In the framework of Hamiltons’s principle we are able to deduce Klein-Gordon equations with negative “mass term” for the field variables electric field E and magnetic induction B. We can conclude from the mathematical structure of the equations that a repulsive interaction appears. The Wheeler propagator can be calculated for the present case by which the time evolution of the field can be discussed. In spite of the situation that these equations have tachyon solutions, the results are in line with the causality principle. As a consequence of the theory, a spontaneous charge disjunction process may rise in the field