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 n field operators at different positions

C_n(x_1, x_2,\ldots,x_n) := \left\langle \phi(x_1) \phi(x_2) \ldots \phi(x_n)\right\rangle =\frac{\int D \phi \; e^{-S[\phi]}\phi(x_1)\ldots \phi(x_n)}{\int D \phi \; e^{-S[\phi]}}

For time-dependent correlation functions, the time-ordering operator 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.

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