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In YM theory, you generally don't take the constant transformations to be gauge transformations, since the constant transformations are generated by the charge operator. If the charge operator generated gauge transformations, it would act trivially on all physical states, which would mean that you couldn't have charges.

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There are such things are large gauge transformations, which I think are related to your question. For example, consider general relativity where the gauge invariance is diffeomorphism invariance. Typically gauge transformations are considered that leave the boundary invariant, but there are also large gauge transformations that for example rescale the ...

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I) The gauge transformation of the real gauge field $V$ reads $$\exp(\tilde{V}) ~=~e^Xe^Ve^Y, \qquad X~:=~i\Omega^{\dagger}, \qquad Y~:=~-i\Omega. \tag{1}$$ Keeping only linear orders in $\Omega$, the BCH formula reads $$\tilde{V}~=~B({\rm ad} V)X+V+B(-{\rm ad} V)Y$$ $$~=~V+\frac{1}{2}[V,Y-X]+B_+({\rm ad} V)(X+Y),\tag{2}$$ where  ...

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Wess-Zumino gauge is a particular choice of gauge where the vector superfield has a particular form and has less components than the generic vector super field. So if i'm free to make a gauge transformation i can choose the components of the chiral super field $\Omega$ in a manner that the sum of the $\theta$ (or any other "$\theta$ component" i want to ...

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