ABSTRACT
Electrodynamics was discovered as a phenomenological theory. Electrodynamics is the low-energy part of the standard model. Solving electrodynamic problems on the computer, guided by the geometrical meaning of the variables has been a decisive factor for the success of the calculation. This chapter considers the scalar potential and vector potential fields that do depend on gauge transformations and as such will give access to the geometry of electrodynamics. The history of the principle of gauge invariance begins with the discovery of the principle of general covariance in general relativity. According to this principle the physical laws should maintain their form for all coordinate systems. With the arrival of quantum mechanics the principle of gauge invariance obtained its final interpretation: gauge invariance should refer to the phase transformations that may be applied on the wave functions.
