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I understand that for a gauge fixing to be valid, it needs to be achievable (i.e., become an identity) continuously through a sequence of allowed gauge transformations of the canonical variables, yet I fail to think of an example of a forbidden choice for some fixing (of an arbitrary example of theory).

What would be such an example? Or, what am I thinking incorrectly?

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    $\begingroup$ I may be misunderstanding what you're saying, but "fixings" like $A=0$, i.e. setting all components of the gauge field to zero, are not valid gauge choices because they can't be reached from configurations that are not pure gauge to begin with. $\endgroup$ – ACuriousMind Jul 22 '16 at 13:39
  • $\begingroup$ @ACuriousMind, right, but in a more general or less trivial sense, I would realize that a fixing is invalid arriving at a contradiction, incompatible system or something like that? I mean, analitically how would one realize if a gauge choice is possible or not? $\endgroup$ – GaloisFan Jul 22 '16 at 13:46
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    $\begingroup$ The question of whether a given gauge choice is globally admissible is in general hard, and called the Gribov problem. There is no generic answer to your question. $\endgroup$ – ACuriousMind Jul 22 '16 at 13:48

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