- #1
DeathbyGreen
- 83
- 15
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
<br /> 4[p'^{\mu}p^{\nu}+p'^{\nu}p^{\mu}-g^{\mu\nu}(p \cdot p'+m_e^2)]<br />
and
<br /> 4[k_{\mu}k'_{\nu}+k_{\nu}k'_{\mu}-g_{\mu\nu}(k \cdot k'+m_{\mu}^2)]<br />
they set m_e=0 and take the dot product of these two to get
<br /> {32e^4}[(p \cdot k)(p' \cdot k')+(p \cdot k')(p' \cdot k)+m^2_{\mu}(p \cdot p')]<br />
When I do this I get
<br /> 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}]<br />
In this scattering problem the two incoming momenta are p and p' and outgoing k and k', 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!
<br /> 4[p'^{\mu}p^{\nu}+p'^{\nu}p^{\mu}-g^{\mu\nu}(p \cdot p'+m_e^2)]<br />
and
<br /> 4[k_{\mu}k'_{\nu}+k_{\nu}k'_{\mu}-g_{\mu\nu}(k \cdot k'+m_{\mu}^2)]<br />
they set m_e=0 and take the dot product of these two to get
<br /> {32e^4}[(p \cdot k)(p' \cdot k')+(p \cdot k')(p' \cdot k)+m^2_{\mu}(p \cdot p')]<br />
When I do this I get
<br /> 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}]<br />
In this scattering problem the two incoming momenta are p and p' and outgoing k and k', 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!