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9 5 The canonical Maxwell's equations are derivable from the Lagrangian $${cal L} = -frac{1}{4}F_{munu}F^{munu} $$ by solving the Euler-Lagrange equations. However : The Lagrangian above is invariant under the gauge transformation $$A_mu to A_mu - partial_mu Lambda(x) $$ for some scalar fiend $Lambda(x)$ that vanishes at infinity. This implies that there will be redundant degrees of freedom in our equations not motion (i.e. Maxwell's equations). Therefore, as I understand gauge fixing, this implies that Maxwell's equations (without gauge fixing) can lead to unphysical predictions. Question : Hence my question is simply are Maxwell's equations (the ones derived from $cal{L}$ above) actually physical, in the sense they do not make unphysical predictions? Example: The general solution to