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$\begingroup$ Thank you, this clears up a lot. However I'd like to check my understanding. You state we must fix some choice of gauge in order to proceed. This then reduces our symmetry group from $\mathcal{G}$ to $G$, which is why ‘Higgsing’ involves an unbroken subgroup $H$ viewed as a subgroup of $G$ rather than $\mathcal{G}$, etc. Am I correct in saying the reason we must fix a gauge because otherwise our system can’t distinguish between gauge equivalent states? $\endgroup$
– leob
Commented Dec 6, 2022 at 16:32

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