Peskin book on QFT question -- 2 integrals for D(x−y)

[Silviu]

Hello! Those who used Peskin's book on qft, in chapter 2, Causality (2.4) there are 2 integrals for $D(x-y)$. Can someone explain to me how does he solve them, as I tried for a bit and didn't manage to do them (actually to get the behavior as $t \to \infty$). Thank you!

 

[strangerep]

IF I've guessed correctly which integrals you mean...

For the 1st one (leading to asymptotic $t\to\infty$ behaviour), see my final post in this old thread.

For the 2nd, that's just a matter of passing to polar-momentum coordinates first, and then doing a contour integral. IIRC, there's a more detailed explanation in Rolnick, Appendix D. (If you want more detailed help, you'll probably need to start a thread in the HW forum and show your work.)