A Second-Quantized Kolmogorov-Chentsov Theorem via the Operator Product Expansion

Understand

We establish a direct connection between two fundamental topics: one in probability theory and one in quantum field theory.

• The first topic is the problem of pointwise multiplication of random Schwartz distributions which has been the object of recent progress thanks to Hairer's theory of regularity structures and the theory of paracontrolled distributions introduced by Gubinelli, Imkeller and Perkowski.
• The second topic is Wilson's operator product expansion which is a general property of models of quantum field theory and a cornerstone of the bootstrap approach to conformal field theory.
• Our main result is a general theorem for the almost sure construction of products of random distributions by mollification and suitable additive as well as multiplicative renormalizations.