# Contour integral trick with propagators

1. Apr 19, 2013

Hi I am struggling trying to see understand the basic propagator integral trick.

$\int \frac{d^{3}p}{(2\pi^{3})}\left\lbrace \frac{1}{2E_{p}}e^{-ip.(x-y)}|_{p_{0}=E_{p}}+\frac{1}{-2E_{p}}e^{ip.(x-y)}|_{p_{0}=-E_{p}}\right\rbrace = \int \frac{d^{3}p}{(2\pi^{3})}\int \frac{dp^{0}}{(i2\pi)}\frac{-1}{p^{2}-m^{2}}e^{-ip.(x-y)}$

I know it can be solved by contour integration about poles $p^{0}=E_{p}$ and $p^{0}=-E_{p}$ respectively but I just can't do it. Any help would be appreciated, I can provide working to what I have done but there doesn't seem much point because I am very confused.

2. Apr 19, 2013

### Chopin

3. Apr 20, 2013