Wilson-Itô diffusions

We introduce Wilson-Itô diffusions, a class of random fields on ${\mathbb{R}}^d$ that change continuously along a scale parameter via a Markovian dynamics with local coefficients. Described via forward-backward stochastic differential equations, their observables naturally form a pre-factorization algebra à la Costello-Gwilliam. We argue that this is a new non-perturbative quantization method applicable also to gauge theories and independent of a path-integral formulation. Whenever a path-integral is available, this approach reproduces the setting of Wilson-Polchinski flow equations.