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The main point of the analysis is the distinction between a classical
electrodynamic theory based on Maxwell equations and on the Lorentz
force on one hand
and theories that are derived from the variational principle
on the other hand.
Gauge transformations are certainly consistent with the former theory
because it relies on fields and the potential is just an auxiliary
mathematical expression. By contrast,
in the variational principle, the electromagnetic potential
is used explicitly in the Lagrangian's interaction term [1,2].
A 23 line text proves that the quantum mechanical structure of the
electromagnetic interaction takes an erroneous form -
Click here.
A further analysis of this problen can be found in the following
article -
Click here.
A not very long paper proves that the above mentioned error is
uncorrectable -
Click here.
In electrodynamics, a gauge transformation applies to the
electromagnetic 4-potential. Inherent contradictions
of this 4-potential are discussed
here.
References:
[1] L. D. Landau and E. M. Lifshitz, The Classical
Theory of Fields (Elsevier, Amsterdam, 2005). (See p. 75.)
[2] J. D. Bjorken and S.D. Drell, Relativistic Quantum
Fields (McGraw-Hill, New York, 1965). (See p. 84.)
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