ABSTRACT
The Maxwell theory of electrodynamics describes the interaction between radiation and charged particles. The electromagnetic fields are described by six quantities, the vector components of E and B. The gauge invariance of the Maxwell equations has been found some posteriori. It was the outcome of a consistent theory for numerous experimental facts. In modern physics invariance principles play a key role in order to classify experimental results. One often postulates some symmetry or some gauge invariance and evaluates the consequences such that one can decide whether the supposed symmetry is capable of correctly ordering the experimental data. The Coulomb gauge is a constraint on the components of the vector potential. The next most commonly used gauge condition is the Lorenz gauge. In this gauge the scalar potential and vector potential are treated on an equal footing. Various derivations of the integer quantum Hall effect are based on the Landau gauge.
