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$$H=H_0+V$$
$$i\frac{\partial }{\partial t}U(t,0)=V_{H_0}(t)U(t,0)$$
$$
e^{iH_{0}t} e^{-iH_{}t} = U(t,0)
$$

main result:

\begin{eqnarray*}
G(t,t')&=&-i\langle \Psi   | T(c_{H}(t)c_{H}^{\dagger}(t'))|\Psi\rangle\\\nonumber
       &=&-i\langle \Psi_0 | U(-\infty,+\infty)T(U(+\infty,-\infty) c_{H}(t)c_{H}^{\dagger}(t') ) |\Psi_0\rangle\\\nonumber
\end{eqnarray*}
with $ |\Psi\rangle=U(0,-\infty)| \Psi _0\rangle $
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