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If, as I asked in this question, a relevant operator in a renormalization group transformation can't be used in a perturbative expansion since it becomes large as the transformations are applied, does this mean that the operator can't be used in 'normal' perturbation theory?

I.e. Is using the renormalization group a way to determine whether or not perturbation theory can be used at all? Or is it only relevant within renormalization groups since without it, the operator remains small?

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