On the Notation of MAXWELL's Field Equations

Introduction The complete set of the equations of James Clerk MAXWELL are known in electrodynamics since 1865. These have been defined for 20 field variables. Later Oliver HEAVISIDE and William GIBBS have transformed this equations into the today’s most used notation with vectors. This has not been happened without ‚background noise‘, then at that time many scientists – one of them has been MAXWELL himself – was convinced, that the correct notation for electrodynamics must be possible with quaternions and not with vectors. A century later EINSTEIN introduced Special Relativity and since then it was common to summarize MAXWELL’s equations with four-vectors. The search at magnetic monopoles has not been coming to an end, since DIRAC introduced a symmetric formulation of MAXWELL’s equations without using imaginary fields. But in this case the conclusion from the Special Theory of Relativity, that the magnetic field originates from relative motion only, can not be hold anymore. The non-symmetry in MAXWELL’s equations of the today’s vector notation may have disturbed many scientists intuitively, what could be the reason, that they published an extended set of equations, which they sometime introduced for different applications. This essay summarizes the main different notation forms of MAXWELL’s equations.