Suppose that I have already calculated the two-point correlation function for a Lagrangian with no interations using the path integral formulation.
\langle \Omega | T[\phi(x)\phi(y)] | \Omega \rangle = \frac{ \int \mathcal{D}\phi \phi(x)\phi(y) \exp[iS_0] }{ \int \mathcal{D}\phi \exp[iS_0] }...