Axiomatics of classical electrodynamics and its relation to gauge field theory

الأصل · EN

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 Dⁱ and Hᵢ, turn out to be a consequence of electric charge conservation, whereas the homogeneous Maxwell equations, expressed in terms of Eᵢ and Bⁱ, are derived from magnetic flux conservation and special relativity theory. The excitations Dⁱ and Hᵢ, by means of constitutive relations, are linked to the field strengths Eᵢ and Bⁱ. Eventually, we point out how this axiomatic approach is related to the framework of gauge field theory.