= Four-point correlation function
{title2=$G^{(4)}(x_1,x_2,x_3,x_4)=\langle T\phi(x_1)\phi(x_2)\phi(x_3)\phi(x_4)\rangle$}
= Four-point function
{synonym}
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.
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