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  • $\begingroup$ Can you give an example of how the phrase 'form invariance on gauge transformation' is used? $\endgroup$
    – knzhou
    Commented Aug 17, 2016 at 3:00
  • $\begingroup$ This appears to be mostly a semantic question which is difficult to answer because the context is lacking. I've never heard "form invariance on gauge transformation", and the usage of the Schrödinger equation and "local phase" implies you want to talk about a specific gauge invariance, since the notion of gauge invariance is more general than "local phases" or, indeed, quantum physics. Finally, I'm not sure what implications you're asking about in the second point - how bad a broken gauge symmetry is again depends on the context, and what it is broken by. $\endgroup$
    – ACuriousMind ♦
    Commented Aug 17, 2016 at 13:13