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A Trouble with Peskin QFT textbook

  1. Dec 3, 2017 #1
    I'm trying to work through a scattering calculation in the Peskin QFT textbook in chapter 5, specifically getting equation 5.10. They take two bracketed terms

    [itex]
    4[p'^{\mu}p^{\nu}+p'^{\nu}p^{\mu}-g^{\mu\nu}(p \cdot p'+m_e^2)]
    [/itex]

    and

    [itex]
    4[k_{\mu}k'_{\nu}+k_{\nu}k'_{\mu}-g_{\mu\nu}(k \cdot k'+m_{\mu}^2)]
    [/itex]

    they set [itex]m_e=0[/itex] and take the dot product of these two to get

    [itex]
    {32e^4}[(p \cdot k)(p' \cdot k')+(p \cdot k')(p' \cdot k)+m^2_{\mu}(p \cdot p')]
    [/itex]

    When I do this I get
    [itex]
    16[2(p' \cdot k)(p \cdot k')+2(k \cdot p)(p' \cdot k')-3(p' \cdot p)(k' \cdot k)-(p' \cdot p)m^2_{\mu}]
    [/itex]
    In this scattering problem the two incoming momenta are [itex]p[/itex] and [itex]p'[/itex] and outgoing [itex]k[/itex] and [itex]k'[/itex], so working in the COM frame I suspect there is a reduction you can make but I can't figure out what it is. Any help is appreciated!
     
  2. jcsd
  3. Dec 3, 2017 #2
    Disregard I got it; I was using a wrong Minkowski metric relation
     
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