Correlation function (quantum field theory)

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.


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

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. 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).