Normal-ordered product
= Normal-ordered product
{title2=$:\mathcal O_1\cdots\mathcal O_n:$}
A <normal-ordered product> of free-field oscillator operators places all <creation operators> to the left of all <annihilation operators>, including the <fermionic sign> required to reorder fermions. Its vacuum expectation vanishes if any nontrivial oscillator factors remain. The <Wick theorem> expresses a free-field <time-ordered product> through these products and all <Wick contractions>.