# Why is it necessary to wrap our contour around the branch cut at $+ im$ in the spacelike Klein-Gordon propagator? (P&S)

This question is in reference to eq. (2.52) on the bottom of page 27 in Peskin and Schroeder.

To evaluate the Klein-Gordon field propagator along a spacelike interval we wrap the contour around the branch cut at $$p=+im$$. My question is (possibly a mathematical one) why it is necessary to move the contour in the first place? The function is analytic along the real axis, which is what we are originally integrating along.

All Peskin and Schroeder want to show is that the integral is non-zero. You could certainly try to exactly compute the integral over the original contour. However, I imagine that it's probably a lot easier to use the new contour wrapped around $$p=im$$. In any case, along the new contour, it is immediately clear that the integral is non-zero because the integrand is always positive. This is not clear along the original contour.