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Stupid question on anomalous magnetic moment of the electron

  1. Nov 13, 2012 #1
    I don't understand one think: when we calculated the correction of the magnetic moment of the electron, we consider only the finite terms of the vertex correction that non depend on the parameter μ. Using Ryder notation , we consider only

    [itex]\bar{u}[/itex](p')(γμ+[itex]\Lambda[/itex]μ(2))u(p)

    but there is also another finite contribution in [itex]\Lambda[/itex]μ(1)
    [itex]\Lambda[/itex]μ(1) = divergent + finite

    , why we don't consider that? some book to view this?
     
  2. jcsd
  3. Nov 13, 2012 #2

    strangerep

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    Science Advisor

    Try Peskin & Schroeder. If I remember correctly, they show how only the ##\Lambda^{(2)}## term you mentioned is relevant to the anomalous magnetic moment, because the ##\Lambda^{(1)}## term goes to 1 as ##q\to 0##. (I'm guessing here that Ryder's ##\Lambda## corresponds to P&S's ##F##.)
     
  4. Nov 14, 2012 #3
    yes,there are two form factors .The first of which becomes 1 in zero momentum transfer case.However I have not read ryder,so may be it is something different.I will reply after taking a look somewhere else.
     
  5. Nov 14, 2012 #4
    thanks . however the [itex]\Lambda[/itex]μ is the vertex correction... when the ryder regularize it, whit the dimensional method, he writes it as the sum of two terms: [itex]\Lambda[/itex](2)μ that is convergent, and [itex]\Lambda[/itex](1)μ that contains the divergent term plus a finite term. Then he calculates the quantity
    [itex]\bar{u}[/itex](p')([itex]\gamma[/itex]μ+[itex]\Lambda[/itex]μ(2))u(p)
    whit q=p'-p (q is the momentum associated to the external photon ) different fo zero. He find the correction:
    g/2=1+α/2π

    but why he doesn't consider the finite term in [itex]\Lambda[/itex](1)μ ?
     
  6. Nov 14, 2012 #5
    thanks now I try to read something
     
  7. Nov 14, 2012 #6
    ok now I understand. I calculate Λ(1)μ : the finite term in it is proportional to the matrix γμ, so it doesn't give any contribution to the magentic moment of the electron ( it contributes only to the form factor F1 )

    certain that the ryder could write instead of "finite" in the expression of Λ(1)μ the term itself, or say something about ...
     
  8. Nov 15, 2012 #7
    they are just the form factors.By taking the non relativistic limit you can interpret F1(0) as the unit of charge(zero momentum transfer case it is 1) and other factor F2(0) which using gordon identity can be interpreted as electron having a magnetic moment (1+F2(0)) which interacts with magnetic field .
     
  9. Nov 15, 2012 #8
    ... I think it's more correct to say that they are connected to form factors, in fact, using the identity of gordon we find that only a part of the finite term [itex]\Lambda[/itex](2)μ contributes to the form factor F2 , and so to the magnetic moment of the electron... anyway thanks to all for your answers, bye
     
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