Ismael Bailleul, Ilya Chevyrev and Massimiliano Gubinelli
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.
Ismael Bailleul, Ilya Chevyrev and Massimiliano Gubinelli. Wilson-Itô diffusions. Papers of Massimiliano Gubinelli, 2023, version 1. https://mgubi.org/papers/paper/wilson-ito-diffusions/
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