4
$\begingroup$

On page 35 of Itzykson-Zuber's textbook on quantum field theory, I am having trouble deriving equation (1-180):

$\displaystyle G_F(0,r) = \frac{i}{(2\pi)^2 r} \int_m^\infty dp \frac{p}{\sqrt{p^2-m^2}} e^{-pr}$

Here $G_F(0,r)$ is the Stueckelberg Feynman propogator $G_F(x) = \frac{-1}{(2\pi)^4} \int d^4 p e^{-i p\cdot x} \frac{1}{p^2 - m^2 + i\epsilon}$, when $x$ is of the form $(0,\vec{x})$ and $|\vec{x}| = r$. Presumably the $i$ in the exponent drops out because we are dealing with complex valued vector $\vec{x}$, but even with that assumption I cannot derive the formula. Any insight is appreciated!

2 Answers 2