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Problem, exercise, anomalous magnetic moment interaction

  1. Aug 4, 2009 #1
    I need to solve an exercise on Quantum Field Theory that reads as follows:

    Supousse that the electron has an anomalous magnetic moment, wich makes the QED Lagrangian
    (density) to have an additional term:

    [tex]
    L'_I(x) = \frac{2ie}{m} \bar{\psi}(x) \sigma^{\alpha\beta} \psi(x) F_{\alpha\beta}(x)
    [/tex]

    where:

    [tex]
    F_{\alpha\beta} = \partial_{\alpha}A_{\beta}(x) - \partial_{\beta}A_{\alpha}(x)
    [/tex]

    1. Find the matrix element (Feynman amplitude) for Moller's dispersion, having in account this additional
    term.

    *****************

    I found that

    [tex]
    \partial_{\alpha}\beta = \sum_k (\mp i k_{\alpha}) A^{\pm}_{\beta}(x)
    [/tex]

    from where, I found that:

    [tex]
    2i\sigma^{\alpha\beta}F_{\alpha\beta}(x) = -i2[\check{K},\check{A}^+ - \check{A}^-]
    [/tex]

    where:

    [tex]
    \check{K},\check{A}^+,\check{A}^-
    [/tex]

    denotes slash operators !!!! (I couldn't find how to draw slash operators here). The problem that I have
    as from here is, that I don't know how to calculate Time Contractions to the operator:

    [tex]
    A^+ - A^-
    [/tex]

    for example, I don't know how to calculate the Feynman propagator to the Time Contraction:

    [tex]
    T\{ A(x)[A^+(y) - A^-(y)] \}
    =
    T\{ [A^+(x) + A^-(x) ][A^+(y) - A^-(y)] \}
    [/tex]


    Does any one knows how to proceed in this case??

    best regards

    Rayo
     
  2. jcsd
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