- #1
DeathbyGreen
- 84
- 16
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!
[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!