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H = kα,n The perturbation expansion becomes 36 3 Applications ∞ Gn,kα (τ, τ ) = l=0 (−i)l+1 l! 7) where we have l Tc {dˆn (τ )Hˆ (τ1 ) · · · Hˆ (τl )ˆ c†kα (τ )} = Tc dˆn (τ ) cˆ†ki αi (τi )tki αi ,ni dˆni (τi ) i=1 ki αi ,ni +dˆ†ni (τi )t∗ki αi ,ni cˆki αi (τi ) cˆ†kα (τ ) . Wick’s theorem can now be applied to correlators of cˆ, cˆ† fields since H is quadratic in these fields, whence the importance of the requirement that the leads be noninteracting. All the contractions involving the first term in Hˆ (τi ) vanish, since dˆn cˆ†ki αi = 0 and dˆni cˆ†kα = 0 for the unconnected system, and the anomalous contractions dˆn dˆni and cˆ†ki αi cˆ†kα vanish because particle number is conserved.

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