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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?

linuxfreebird
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  • 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? – John Rennie Mar 17 '14 at 18:25
  • @JohnRennie that certainly sounds like a reasonable way of putting it. – Danu Mar 17 '14 at 18:51
  • @JohnRennie Yes, that is what I mean by Global Charge Conservation. Can you suggest an edit to the question for clarity? – linuxfreebird Mar 17 '14 at 19:46
  • 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? – Frederic Brünner Mar 17 '14 at 20:30
  • @FredericBrünner I think that answer to your question is related to this question: http://physics.stackexchange.com/questions/103535/is-there-a-fourth-component-to-the-electric-field-and-magnetic-field – linuxfreebird Mar 17 '14 at 20:43
  • I do not see the relation. – Frederic Brünner Mar 17 '14 at 20:51
  • I not sure, but I believe that breaking gauge invariance reveals a fourth component in the electromagnetic field. – linuxfreebird Mar 17 '14 at 20:53
  • Gauge invariance allows one to remove one component of the gauge field by fixing the gauge. I still do not see the relation to this question – Frederic Brünner Mar 17 '14 at 21:00
  • I recommended attempting to solve this question: http://physics.stackexchange.com/questions/103664/express-maxwells-equations-in-terms-of-dipole-field-equations I am having trouble redoing the math, but I remember when I transformed maxwell's equations from monopole sourced to dipole sourced, there was a fourth component that appeared in the field equations and it broke charge conservation relative to the dipole field density. – linuxfreebird Mar 17 '14 at 21:13
  • @FredericBrünner I rewrote the following question: I finally was able to answer the following question: http://physics.stackexchange.com/questions/103664/dipole-transformation-of-maxwells-equations Please investigate this question, because there is a fourth component in the field. I was able to find the correct dipole transformation of Maxwell's equations. This new field equation has a fourth component in the field equations which breaks the dipole charge conservation(fictitious dipole conservation). – linuxfreebird Mar 18 '14 at 15:56

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