# Correlation function in QFT

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bengeof

## Main Question or Discussion Point

Hi
I would be happy if anyone helped me understand what the physical meaning of n-particle correlation function in QFT is ?

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king vitamin
Gold Member
Are you familiar with operators, observables, and matrix elements in introductory quantum mechanics?

The correlation functions have many different physical interpretations depending on which correlation function you're asking about. This is because your physical observables (which are operators) can be built out of quantum fields, so the expectation values, variances, probabilities, and matrix elements of your theory are made out of correlation functions. As some definite examples:

The LSZ formula relates certain correlation functions to scattering and decay probabilities: https://en.wikipedia.org/wiki/LSZ_reduction_formula

The Källén–Lehmann spectral representation of a field tells you about the physical spectrum of the theory by telling you the energy of excitations created by the field: https://en.wikipedia.org/wiki/Källén–Lehmann_spectral_representation

The Kubo formula tells you how one operator changes if you perturb your system by a different operator (since all operators are built out of fields, these are also field correlators): https://en.wikipedia.org/wiki/Kubo_formula

bengeof
Thank you for your response. Yes my background is QM as done in Griffiths( So yes I have a background of operators, observables and scattering matrix), Classical fields as done in Goldstein and Particle physics as in Griffiths. Griffiths actually works out Feynman rules for QED and QCD.

2 point function is interpreted as propagation amplitude of a particle from x to y, so how does one interpret a n-point correlation function. I know wick's theorem is used to break it down to sums and products of two point functions? isn't that how it works?

king vitamin
Gold Member
The usual interpretation seen often in an introductory quantum field theory course is the calculations of particle scattering or decay using the LSZ formula I mentioned above. This formula relates an ("amputated") N-point function to a scattering/decay process involving N particles coming both "in" and "out." For example, let's say you have a theory of scalar particles, call them mesons. If you want the scattering amplitude of two mesons coming in and two mesons coming out, it is related to the 4-point function.

But once again, since all operators in your theory can be written in terms of the fields, and expectation values of operators are then N-point functions, they show up everywhere.

bengeof