The Physical Meaning of Gauge Transformations in Classical   Electrodynamics
  The structure of electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potential is defined uniquely. Therefore, the approach where Maxwell equations and the Lorentz law of force are regarded as cornerstones of the theory is not equivalent to the one described above. 
E. Comay