 Four-point correlation function

The four-point correlation function measures a time-ordered product of four field insertions. For a centered scalar field its disconnected terms are the three products of two-point functions, and subtracting those products leaves the connected correlation function. In a free Gaussian scalar vacuum the connected four-point function vanishes, by Wick's theorem, so only the three paired products remain. The connected four-point function of phi-fourth theory starts with one quartic vertex; amputation removes its external propagators. The full correlator, its connected part and the four-point one-particle-irreducible correlation function should therefore be distinguished.