Axiomatics of classical electrodynamics and its relation to gauge field theory

We give a concise axiomatic introduction into the fundamental structure of classical electrodynamics: It is based on electric charge conservation, the Lorentz force, magnetic flux conservation, and the existence of local and linear constitutive relations. The inhomogeneous Maxwell equations, expressed in terms of D and Hi , turn out to be a consequence of electric charge conservation, whereas the homogeneous Maxwell equations, expressed in terms of Ei and B, are derived from magnetic flux conservation and special relativity theory. The excitations D and Hi , by means of constitutive relations, are linked to the field strengths Ei and B. Eventually, we point out how this axiomatic approach is related to the framework of gauge field theory. E-Mail: [email protected], [email protected], [email protected] 1Edited by C.E. Baum, Air Force Research Laboratory, Kirtland Airforce Base, New Mexico, USA