[QUE/QFT-11006] QFT-PROBLEM

The Feynman propagator for Klein Gordon field corresponds to \(i\epsilon\) prescription as given below $$ \Delta_F(x-y) = \int d^4k {\exp(ikx)\over k^2-m^2+2i\epsilon k_0}~~,~~\epsilon>0 $$

• [(a)] Show the poles of the integrand in complex $k_0$ plane for $\epsilon>0$.
• [(b)] Evaluate the $k_0$ integral and write your answer for the Feynman propagator as integrals overs space components of momentum $k=(k_0\vec{k})$