Gauge invariance of the electromagnetic field implies local charge conservation. If the gauge is no longer invariant, then the electromagnetic field must no longer conserve charge locally. Is it possible either physically or mathematically, to break local charge conservation, but still enforce global charge conservation? Charge can be created and destroyed at will, but the total amount of charge created at any given time is zero?
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asked Mar 17, 2014 at 16:56
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$\begingroup$ It isn't obvious to me what you mean by global and local charge conservation. Would global but not local conservation mean charge conservation could be violated within some region of space provided it was simultaneously violated in the opposite sense in some other (spacelike separated?) region of space? $\endgroup$– John RennieCommented Mar 17, 2014 at 18:25
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$\begingroup$ @JohnRennie that certainly sounds like a reasonable way of putting it. $\endgroup$– DanuCommented Mar 17, 2014 at 18:51
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$\begingroup$ @JohnRennie Yes, that is what I mean by Global Charge Conservation. Can you suggest an edit to the question for clarity? $\endgroup$– linuxfreebirdCommented Mar 17, 2014 at 19:46
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$\begingroup$ The conservation of electric charge is related to the presence of a global $U(1)$ symmetry. As long as you have a global invariance, your charge is conserved. Why would charge not be conserved when you do not have a local (gauge) symmetry? $\endgroup$– Frederic BrünnerCommented Mar 17, 2014 at 20:30
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$\begingroup$ @FredericBrünner I think that answer to your question is related to this question: physics.stackexchange.com/questions/103535/… $\endgroup$– linuxfreebirdCommented Mar 17, 2014 at 20:43
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