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.

<math>\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</math>

Sometimes, the time-ordering operator <math>T</math> 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 <math>n</math> (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 functionTemplate:Quantum-stub

See Also:

• (PN Sequences)