= State-operator correspondence for Virasoro primaries
{title2=$|\mathcal O\rangle=\mathcal O(0)|0\rangle$}
For a <primary operator>, $T(z)\mathcal O(0)\sim h\mathcal O(0)/z^2+\partial\mathcal O(0)/z$. Taking the residue against $z^{n+1}$ gives the weight for $n=0$, the derivative descendant for $n=-1$, and zero for every $n>0$. Conversely the absence of positive-mode actions excludes higher poles in this operator product and gives the primary transformation law. The antiholomorphic argument is identical. Thus <primary states> and <primary operators> correspond under <radial quantization>.
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