= Operator product expansion
{title2=OPE}
{wiki}
An operator product expansion rewrites nearby local <local field operators> as a sum of local <local field operators> with separation-dependent coefficient functions: $\mathcal O_i(x)\mathcal O_j(0)=\sum_k C_{ij}{}^k(x)\mathcal O_k(0)$, in the appropriate short-distance or convergent <correlation function> sense. The coefficients can contain singular terms, but regular terms and descendants also carry information.
For example, the <stress-tensor operator-product expansion> in a two-dimensional <conformal field theory> contains the identity contribution fixed by the <central charge>, followed by the <stress-energy tensor> and its derivative. Substituting an operator product expansion into a <correlation function> reduces a nearby pair to a sum of simpler insertions. Its domain and convergence properties depend on the theory and operator configuration; a schematic short-distance equality is not an unrestricted multiplication rule at every separation.
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