# Why do disconnected diagrams not contribute to the S matrix?

I've read somewhere that disconnected diagrams do not contribute to the S-matrix. I don't see why this is the case. I do know why vacuum bubbles do not contribute: given a generating functional for a scalar field the n-point correlation function follows from: $$G(x_1, \dots,x_n) = \frac{1}{i^n}\frac{\delta}{\delta J(x_1)}\frac{\delta}{\delta J(x_n)}Z_0[J]|_{J=0}$$ If you treat the generating functional in perturbation theory, expaning out the denominator of $$Z[J] = \frac{\int\mathcal{D}\phi\exp(iS + i\int J\phi dx)}{\int\mathcal{D}\phi\exp(iS)}$$ will cancel all vacuum bubbles from the numerator. Does something similar hold for the disconnected diagrams?

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Have a look at Peskin and Schroeder section 4.6. –  user7757 Jan 24 '13 at 5:52