Correlation function (quantum field theory) - Alchetron, the free social encyclopedia

In quantum field theory, the (real space) n-point correlation function is defined as the functional average (functional expectation value) of a product of n field operators at different positions

C n ( x 1 , x 2 , … , x n ) := ⟨ ϕ ( x 1 ) ϕ ( x 2 ) … ϕ ( x n ) ⟩ = ∫ D ϕ e − S [ ϕ ] ϕ ( x 1 ) … ϕ ( x n ) ∫ D ϕ e − S [ ϕ ]

For time-dependent correlation functions, the time-ordering operator T is included.

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.

The correlation function can be interpreted physically as the amplitude for propagation of a particle or excitation between y and x. In the free theory, it is simply the Feynman propagator(for n=2). [For more information see 'An Introduction to Quantum Field Theory' by Peskin & Schroeder, Section 4.2 : Perturbation Expansion of Correlation Functions]

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Correlation function (quantum field theory) Wikipedia

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