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Charge Conservation

  1. Jun 4, 2005 #1
    So, I was just introduced to the Klein-Gordon equation. I've been asked to derive the continuity equation for charge density and current density. I am having trouble understanding this. If I were to derive a continuity equation involving charge, doesn't this say that charge is conserved locally?

    Obviously, I am confused. My current thinking says that charge cannot be locally conserved in quantum mechanics since things "jump" around and tunnel. However, I suppose I could also make the same argument about probability conservation---yet we do believe that probability is conserved in quantum mechanics.

    Could someone elighten me with a general discussion on this topic?
     
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  3. Jun 4, 2005 #2

    dextercioby

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    How about applying Noether's theorem in the classical fields and the current 4-vector is automatically conserved ?

    Daniel.
     
  4. Jun 4, 2005 #3
    I'm not disputing the result; I'm seeking an explanation as to why I should expect charge to be locally conserved in light of the fact the QM is a nonlocal theory. That fact that the result can be dervied mathematically, in a variety of ways, does not answer this question (at least in my humble opinion).

    Looking forward to your response (and the responses of others as well).
     
    Last edited: Jun 4, 2005
  5. Jun 4, 2005 #4

    dextercioby

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    Charge is not locally conserved,but globally.It comes from a rigid global symmetry of the (electrically) charged KG field's Lagrangian action.

    Incidentally,when coupling to the abelian gauge field,the electric charge conservation follows from gauge/local symmetry.

    But for a free charged field,it's a global symmetry.

    Daniel.

    P.S.That "KG" is not Kevin Garnett,though under certain circumstances,TD stands for Tim Duncan and not Theory Development.
     
  6. Jun 5, 2005 #5

    Meir Achuz

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    Even in Classical EM, the continuity eq. does not prove charge conservation locally, but only when integrated using the div theorem.
     
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