# Green function for interacting system

If we can diagonalize our interacting Hamiltonian then can we write a Green's function like we do for a non-interacting system? Green's function here means Matsubara in frequency-momentum space, $G(w,k)=w-E(k)$.

• There are many different kinds of Green's functions (time-ordered, retarded/advanced, Matsubara, Keldysh, etc.), and I don't think it is obvious what your notation means. Perhaps you could add the definitions of the quantities that you refer to, and provide some more context for your question? – jabirali Dec 4 '14 at 6:01

yes you can write the green function in $G(w,k)=w-E(k)$ form if you have diagnolized your hamiltonian