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. It is a linguistic term suggesting a "relation" between two states (in the same dynamics) and has no connection whatsoever with the correlation function of the subject of Statistics.
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 function is 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).
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