Axiomatics of classical electrodynamics and its relation to gauge field theory

Gronwald, Frank; Hehl, Friedrich W.; Nitsch, Jürgen

Axiomatics of classical electrodynamics and its relation to gauge field theory

Authors

Gronwald, Frank

Hehl, Friedrich W.

Nitsch, Jürgen

Description

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 {\it inhomogeneous} Maxwell equations, expressed in terms of $D^i$ and $H_i$, turn out to be a consequence of electric charge conservation, whereas the {\it homogeneous} Maxwell equations, expressed in terms of $E_i$ and $B^i$, are derived from magnetic flux conservation and special relativity theory. The excitations $D^i$ and $H_i$, by means of constitutive relations, are linked to the field strengths $E_i$ and $B^i$. Eventually, we point out how this axiomatic approach is related to the framework of gauge field theory.
24 pages latex, 4 figures