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(adsbygoogle = window.adsbygoogle || []).push({});

[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!

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# A Trouble with Peskin QFT textbook

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