# When are the OPE relevant?

I've seen OPEs commonly used in 2d CFT, it's quite apparent to me that, in that case, it dresses a bridge between the algebraic and the operator formalism especially when combined with radial ordering and the use of contour integral. Even more powerful in the minimal models where it leads to the bootstrap equations and the resolution of the 3 pt functions. I also heard that OPE are sometimes used in other circumstances, for instance in the QCD chapter of Peskin & Schroeder's book but I don't recall the motive. I'd be curious to know what generally it is relevant to decompose the products of operators into an "operator basis" ie. associate an algebra to the space of operators.

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In P&S, the OPE was used to discuss Deep Inelastic scattering. It also discusses $e^+e^-$ scattering using OPEs –  Prahar Jun 6 '13 at 22:12