[QUE/QFT-11] Feynman Propagator

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

1. Show the poles of the integrand in complex \(k_0\) plane for \(\epsilon>0\).
2. Evaluate the \(k_0\) integral and write your answer for the Feynman propagatoras integrals overs space components of the four momentum \(k=(k_0,\vec{k})\).