ABSTRACT
Maxwell's description of electromagnetic interactions is a field theory. This fact played a leading role in the development of theories of fundamental interactions since Maxwell. Maxwell's theory of electricity and magnetism was therefore a tremendous achievement. He reduced this large variety of phenomena to the knowledge of essentially two relations, the material relations between B and H and D and E, which must be known experimentally in order to apply his theory. The Maxwell-Lorentz equations are consistent with the Lorentz relativity of velocity; they are invariant under the Lorentz group of transformations. This is an experimental fact: two inertial observers can use the same form of these equations and find that their description of the observed phenomena is correct. The transformation properties of the field strengths follow trivially from those of the potential in the Lorentz gauge. In solving the Maxwell-Lorentz equations one is led into rather complex expressions.
