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What is charge? i do not want to hear that it is of two kind

  1. Mar 11, 2012 #1
    what is charge?
    i do not want to hear that it is of two kind :positive and negative
    i just want to know if there is a fundamental definition of charge like mass?
  2. jcsd
  3. Mar 11, 2012 #2
    Re: charge

    Hi nouvea_riche,

    Charge is a fundamental property of things. What fundamental definition of mass do you mean? That might make it easier to formulate an answer in the same way.
  4. Mar 12, 2012 #3


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    Re: charge

    It's a bit complicated.

    If you look at Maxwells's theory you see the 'e' in the equation. This is not really a charge but a coupling constant. The charge Q is defined in terms of the charge density ρ and is conserved due to Noether's theorem.

    [tex]Q = e\int_{\mathbb{R}^3}d^3x\,\rho(x) [/tex]

    [tex]\frac{dQ}{dt} = 0[/tex]

    In QED the charge is no longer arbitrary but can be defined in terms of the electron and positron field ψ. There are now operators ρ and Q:

    [tex]\rho = j^0 = \psi^\dagger \psi[/tex]

    Again Q is defined as an integral and is conserved, i.e.

    [tex][H,Q] = 0[/tex]

    The proof in QED goes beyond Noether's theorem b/c we have to deal with (renormalized) operators instead of classical fields.

    What we observe in nature are states (electrons, positrons, ...) which are eigenstates of Q, i.e.

    [tex]Q|\psi\rangle = q|\psi\rangle = ne|\psi\rangle[/tex]

    with n=0,±1,±2,...

    Afaik there is no proof in standard QED that the eigenvalues q of Q are always quantized in integer units of e, i.e. that q=ne must always hold. In addition afaik there is no proof that physical states are always eigenstates of Q, i.e. that something like

    [tex]|\psi\rangle = |n=1\rangle + |n=2\rangle;\;\;Q|n\rangle = n|n\rangle[/tex]

    must not exist.
    Last edited: Mar 12, 2012
  5. Mar 12, 2012 #4
    Re: charge

    James Clerk Maxwell defined charge as a discontinuity of polarization. He apparently drew that idea from Clausius Mossotti who earlier built a theory of electricity based on how a medium can be polarized.
  6. Mar 13, 2012 #5


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    Science Advisor

    Re: charge

    there are some reasons (especially in non-abelian gauge theories) that total charge is always zero for physical states, i.e. Q|phys> = 0, but this is not completely rigorous; note: in QCD is color-neutrality is different from color-confinement!
  7. Mar 13, 2012 #6
    Re: charge

    like resistance to acceleration for mass
  8. Mar 13, 2012 #7
    Re: charge

    all maths,i need theoretical
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