I've been learning Green's Functions (Zero-Temprature) from Fetter and Walecka's Quantum Theory of Many-Particle Systems, and find it hard to understand the proof of Goldstone's Theorem, in page 111, the equation is: $$[E-E_0]^{(n)}=⟨\Phi_0|\hat{H_1}\frac{1}{E_0-\hat{H_0}+i\epsilon n\hbar}\hat{H_1}\frac{1}{E_0-\hat{H_0}+i\epsilon (n-1)\hbar}...\hat{H_1}\frac{1}{E_0-\hat{H_0}+i\epsilon \hbar}\hat{H_1}|\Phi_0⟩_C$$ where C stands for connected. He noted that the limitation to connected diagrams ensures that $|\Phi_0⟩$ can not appear as an intermediate state and is nondegenerate. I'm confused with this statement.