Keeping aside Quantum Electro-Dynamics (QED), I believe there should exist a General Relativity like geometrical interpretation of electro-magnetic forces experienced and caused by electrical charges. There could be an all permeating electro-magnetic field in our universe which is perturbed or better said distorted by the presence of charged particles in it. This distortion is detected only by particles which respond to the perturbations in the field and are created by this field.
It is obvious that these would be electric charges. Just like matter follows geodesics in the curved space-time geometry giving the notion of the presence of a force called gravity; linearly and uniformly travelling charges respond to the curvatures caused in the electromagnetic field fabric by other charges and are attracted or repelled by them.
More on this Later. Let the plausibility of this idea settle-in for the time being.