# Correlation function (quantum field theory)

In quantum field theory, the (real space) n-point correlation function is defined as the functional average (functional expectation value) of a product of ${\displaystyle n}$ field operators at different positions

${\displaystyle C_{n}\left(x_{1},x_{2},\ldots ,x_{n}\right):=\left\langle \phi (x_{1})\phi (x_{2})\cdots \phi (x_{n})\right\rangle ={\frac {\int {\mathcal {D}}\phi \;e^{-S[\phi ]}\phi (x_{1})\cdots \phi (x_{n})}{\int {\mathcal {D}}\phi \;e^{-S[\phi ]}}}}$

For time-dependent correlation functions, the time-ordering operator ${\displaystyle T}$ is included.

Correlation functions are also called simply correlators. Sometimes, the phrase Green's function is used not only for two-point functions, but for any correlators.

The correlation function can be interpreted physically as the amplitude for propagation of a particle or excitation between y and x. In the free theory, it is simply the Feynman propagator (for n = 2).[1]