  We formulate an "action principle" for the operator product expansion (OPE)
describing how a given OPE coefficient changes under a deformation induced by a
marginal or relevant operator. Our action principle involves no ad-hoc
regulator or renormalization and applies to general (Euclidean) quantum field
theories. It implies a natural definition of the renormalization group flow for
the OPE coefficients and of coupling constants. When applied to the case of
conformal theories, the action principle gives a system of coupled dynamical
equations for the conformal data. The last result has also recently been
derived (without considering tensor structures) independently by Behan
(arXiv:1709.03967) using a different argument. Our results were previously
announced and outlined at the meetings "In memoriam Rudolf Haag" in September
2016 and the "Wolfhart Zimmermann memorial symposium" in May 2017.
