Understanding the Klein-Gordon Propagator and its Satisfying Equation

[WarnK]

Homework Statement

Homework Equations

Show that the KG propagator
$$G_F (x) = \int \frac{d^4p}{(2\pi)^4} e^{-ip.x} \frac{1}{p^2-m^2+i\epsilon}$$
satsify
$$(\square + m^2) G_F (x) = -\delta(x)$$

The Attempt at a Solution

I get
$$(\square + m^2) G_F (x) = - \int \frac{d^4p}{(2\pi)^4} (p^2-m^2) e^{-ip.x} \frac{1}{p^2-m^2+i\epsilon}$$
but where do I go from there?

 

[pam]

Cancel the numerate and denominator p^2-m^2.
The i epsilon is just a direction how to take the contour, and is negligible here.
The remaining integral is \delta^4.

 

[malawi_glenn]

how does (p^2-m^2)/(p^2-m^+i*epsilon) cancel?

I would try to do the limit of epsilon -> 0+

 

[pam]

how does (p^2-m^2)/(p^2-m^+i*epsilon) cancel?

I would try to do the limit of epsilon -> 0+

That's what
"The i epsilon is just a direction how to take the contour, and is negligible here."
means.