S-matrix and free electron Green's function

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The switching of the fermion operator from Heisenberg rep to interaction rep is a bit confusing around 28:30. I assume the c_lambda(t) on the two sides are in different reps, but it's not clear to me that at which time they are identical

飞白-yi
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21:42
How is this formula derived? It seems that there is no proofs of this in the previous lectures. If it's so then where could I get an explanation?

AlexDreamy