Due to translational symmetry, it is only necessary to consider G ( x , τ τ ∣ ∣ 0 , 0 ) for τ τ > 0 , given by G ( x , τ τ ∣ ∣ 0 , 0 ) = 1 Z ∑ ∑ α α ′ e − − β β E α α ′ ⟨ ⟨ α α ′ ∣ ∣ ψ ψ ( x , τ τ ) ψ ψ ¯ ¯ ( 0 , 0 ) ∣ ∣ α α ′ ⟩ ⟩ . Inserting a complete set of eigenstates gives G ( x , τ τ ∣ ∣ 0 , 0 ) = 1 Z ∑ ∑ α α , α α ′ e − − β β E α α ′ ⟨ ⟨ α α ′ ∣ ∣ ψ ψ ( x , τ τ ) ∣ ∣ α α ⟩ ⟩ ⟨ ⟨ α α ∣ ∣ ψ ψ ¯ ¯ ( 0 , 0 ) ∣ ∣ α α ′ ⟩ ⟩ .