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In QFT, specifically in scattering processes, what is the physical significance of the poles / residues of the $N$-point correlation function? And why?

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Related: physics.stackexchange.com/q/29532/2451 –  Qmechanic Apr 27 '13 at 18:54

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In the frequency domain, poles of the correlation function $G^{r}(\omega)$ correspond to resonance frequencies. In many body theory, such resonances describe metastable oscillations relating to quasi-particles characterized by self-energies.

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