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A gauge theory has internal degrees of freedom that do not affect the foretold physical outcomes of the theory. The theory has a Lie group of *continuous symmetries* of these internal degrees of freedom, *i.e.* the predicted physics under any transformation in this group on the degrees of freedom. Examples include the $U(1)$-symmetric quantum electrodynamics and other Yang-Mills theories wherein non-Abelian groups replace the $U(1)$ gauge group of QED.

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How to prove that Faddeev-Popov ghosts are unnecessary for Yang-Mills theory with axial gauge?

The gist of the Faddev-Popov procedure is that a gauge condition of the form $$ G(A_\mu) = S-w(x) $$ (where in the modified Lorentz gauge $ S= \partial_\mu A^a_\mu $ or in the axial gauge $S= n_\mu A_ …
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