Correlation function (quantum field theory)

For other uses, see Correlation function (disambiguation).

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In quantum field theory, the matrix element computed by inserting a product of operators between two states, usually the vacuum states, is called a correlation function.

$\mathrm{Cor}(x_1,\dots x_n) = \langle 0 | \hat L_1(x_1)\hat L_2(x_2)\dots \hat L_n(x_n) |0 \rangle$

Sometimes, the time-ordering operator T is included. Time ordering appears in the path integral formulation and the Schwinger-Dyson equations.

Without time ordering, they are called Wightman functions/Wightman distributions.

Depending on n (the number of inserted operators), the correlation functions are called one-point function (tadpole), two-point function, and so on.

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.

See also connected correlation function, one particle irreducible correlation function, Green's function (many-body theory).