1 An axiomatic, geometric, formulation of electromagnetism with only one axiom: the field equation for the bivector field F.

An axiomatic, geometric, formulation of electromagnetism with only one axiom: the field equation for the bivector field F. In this paper we present an axiomatic, geometric, formulation of electromagnetism with only one axiom: the field equation for the Faraday bivector field F. This formulation with F field is a self-contained, complete and consistent formulation that dispenses with either electric and magnetic fields or the electromagnetic potentials. All physical quantities are defined without reference frames, i.e., they are geometric four dimensional (4D) quantities or, when some basis is introduced, every quantity is represented as a 4D coordinate-based geometric quantity comprising both components and a basis. The observer independent, expressions for the stress-energy vector T (n) (1-vector), the energy density U (scalar), the Poynting vector S and the momentum density g (1-vectors), the angular momentum density M (bivector) and the Lorentz force K (1-vector) are directly derived from the field equation for F. The local conservation laws are also directly derived from the field equation. We also briefly consider the corresponding Lagrangian formulation that exclusively deals with F. It is shown that this geometric formulation is in a full agreement with the Trouton-Noble experiment. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows and only a kind of union of the two will preserve an independent reality. H. Minkowski