= Two-field scalar Wick identity
{title2=$T\{\phi(x)\phi(y)\}=:\phi(x)\phi(y):+\Delta_F(x-y)\mathbf1$}
For a free real <scalar field>, split $\phi=\phi^{(+)}+\phi^{(-)}$ into annihilation and creation parts. Moving the creation operators left gives $\phi(x)\phi(y)=:\phi(x)\phi(y):+[\phi^{(+)}(x),\phi^{(-)}(y)]$. The <commutator> is the <Wightman function>. Choosing either time order gives the displayed identity with the <Feynman propagator>. It is an identity of <operator-valued distributions>; coincident-point products need a suitable prescription.
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