We develop a framework for the rigorous description of general local composite observables in Euclidean quantum field theories. The approach is nonperturbative and combines renormalization group ideas with techniques of stochastic analysis. Via renormalization dictated by sufficiently precise approximate solution theory of corresponding flow equations, we construct various highly singular observables of the massive sine–Gordon model on the full space up to β^2<6π, including polynomials, derivatives and vertex fields. Applications of the approach include a simple, direct proof of smoothness of observable-inserted correlation functions, and verification that the constructed objects satisfy a version of the prefactorization algebra axioms adapted to our setting. 

 

Based on joint work with M. Gubinelli.