Lorentz invariant relativistic electrodynamics in the Clifford algebra formalism. The formulation with bivector field F

Abstract

In this paper we present the formulation of relativistic electrodynamics (independent of the reference frame and of the chosen system of coordinates in it) that uses 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 or, when some basis is introduced, every quantity is represented as a coordinate-based geometric quantity comprising both components and a basis. The new, observer independent, expressions for the stress-energy vector T(n), the energy density U, the Poynting vector S and the momentum density g, the angular momentum density M and the Lorentz force K are directly derived from the field equations with F.