Computing Correlation functions

[gremory]

TL;DR

How do i understand what a correlation function is and what i can do with it

Hello, recently I'm learning about correlation functions in the context of QFT. Correct me with I'm wrong but what i understand is that tha n-point correlation functions kinda of describe particles that are transitioning from a point in space-time to another by excitations on the field. So, what i need help is that i have a field and this field is solution to the classic equations of motion (i.e. it was obteined via hamilton-lagrange equations of motion). I want to know, if it's possible, how to use this field in a correlation function, if it would have any physical meaning and if i can obtain anything from it. Meaning, how do i use a specific field solution and get some sort of result (in this case a probability i guess). I hope I've been clear because english is not my native language so maybe something is not right or confusing.

 

[WernerQH]

I want to know, if it's possible, how to use this field in a correlation function, if it would have any physical meaning and if i can obtain anything from it.

Correlation functions are what QFT is all about. In the simple case of an harmonic oscillator the propagator $\langle x(t) x(0) \rangle$ describes how the coordinate at one time is correlated with the coordinate at a later time $t$. A photon propagator describes how the field at one point in space-time is related to a current at another point. Because of interactions (for example with electrons) these correlations become modified; they are not the same as the Green's function you can derive from a simple Lagrangian that describes only non-interacting ("raw") particles. But compounding the simple Green's functions in the form of Feynman diagrams provides a way to compute the correlations of the "dressed" particles in the real world. Leading to a refractive index, for example.

A long time ago a tutor suggested a book to me that I found very enlightening: "Elements of Advanced Quantum Theory" by John Ziman (CUP 1969). Perhaps you can find it in a library.