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[QUE/QFT-11006] QFT-PROBLEM

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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 $k=(k_0\vec{k})$

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