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Peskin & Schroeder QFT 5.6 Need help!

  1. Dec 6, 2009 #1
    Hey!

    I need some help for problem 5.6 (b) in Peskin + Schroeder QFT. I can't get rid of the term including three gamma matrices in my amplitude.

    I get two terms of the form:

    \frac{-\gamma^{\nu}*\slash{k_2}*\gamma^{\mu} + 2\gamma^{\nu}p_1^{\mu}}{-2*p_1*k_2}

    and the same with k_1 <-> k_2 and \nu <-> \mu.

    How can I evaluate the first term in the numerator using the Fierz identiy from 5.3?

    Thanks in advance!!

    Philip
     
  2. jcsd
  3. Dec 6, 2009 #2
    Sorry here again the equation:

    [tex]\bar{u_R}(p_2)\frac{-\gamma^{\nu}k_2\!\!\!/\gamma^{\mu} + 2\gamma^{\nu}p_1^{\mu}}{-2p_1k_2}u_R(p_1) [/tex]

    + the same term with [tex] k_1 <-> k_2 [/tex] and [tex] \mu <-> \nu [/tex]

    This is one factor in my amplitude (from the propagator). How can I apply the Fierz identity?

    I could solve 5.3 adding [tex]1 = \frac{1}{4}[\gamma_{\mu}]_{ab}[\gamma^{\mu}]_{ba}[/tex]

    and then apply the Fierz identity. The problem is that in 5.6 I get this term consisting of 3 matrices.
     
    Last edited: Dec 6, 2009
  4. Dec 6, 2009 #3
    Well if I calculate a bit I get finally something like

    [tex]
    k_1\!\!\!/u_R(p_1)\bar{u}_R(k_1)
    [/tex]

    and further terms of that type. What can i do with that?
     
  5. Dec 7, 2009 #4
    Please remove the thread!
     
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