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I am learning the basics of QFT at the moment. Could someone explain to me, in the case for any number of scalar fields, the difference between correlation functions and scattering amplitudes please?

Correlation functions <0|T(\phi_{1}....\phi{n})|0>

Does one always write the mathematical expression in terms of coordinate space? What does it actually measure? Once we have calculated it, what is its significance?

Scattering Amplitude?

I read that one always need to impose momentum conservation at each vertex. But does this still hold when we have undetermined loop momentum between these vertices? What does the scattering amplitude actually measure? How is it related to the correlation function?

Many thanks!

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# Correlation functions vs. Scattering Amplitude

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