Inherent gauge inconsistencies within electrodynamics

New results of gauge transformations are discussed. An important element of the analysis is the distinction between classical electrodynamics based on Maxwell equations together with the Lorentz force versus electrodynamic theories that are derived from the variational principle. The results show that gauge transformations are acceptable in a theory of the first kind. On the other hand, a straightforward analysis proves that gauge transformations are inconsistent with the variational principle. This conclusion holds for the quantum domain and for classical electrodynamics as well. Several specific examples substantiate this inconsistency. The results are compatible with the negative opinion of Dirac, Feynman, and others regarding the mathematical structure of quantum electrodynamics.