Correlation function (quantum field theory)

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In quantum field theory, correlation functions generalize the concept of correlation functions in statistics. In the quantum mechanical context they are computed as the matrix element of a product of operators inserted between two vectors, usually the vacuum states.

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. The correlation functions are often 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).