Electromagnetism as a purely geometric theory

Abstract This research article derives a nonlinear generalization of Maxwell’s equations from a variational approach, when the action measures the variability of the metric tensor. The proper space is a Weyl space, where the covariant derivative of the metric tensor does not need to vanish. The Lorentz force law is derived from the same metrics as a geodesic equation. The charge density is shown to obey a covariant wave equation, which indicates that charge density is a field, which propagates at the speed of light. This viewpoint promotes the wave-picture of the electron. The results indicate that the Dirac equation is a geometric equation as well. As the electrodynamic force, i.e. the Lorentz force can be related directly to the metrical structure of spacetime, it directly leads to the explanation of the Zitterbewegung phenomenon and quantum mechanical waves as well.