= Two-field Wick contraction identity
{title2=$T\phi(x)\phi(y)=:\phi(x)\phi(y):+D_F(x-y)$}
Split a free scalar field into its annihilation and creation parts. For $x^0>y^0$, changing the product into <normal ordering> adds $[\phi^{(+)}(x),\phi^{(-)}(y)]$, the positive-frequency two-point function. For the opposite ordering interchange the two points. Their combination is the <Feynman propagator>, equal to the vacuum expectation of the <time-ordered product>. Iterating this identity gives the scalar <Wick theorem>.
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