An analytic approach to quantum gauge theories

Seminar in Mathematics

Abstract: Quantum gauge theories (QGTs) play a central role in our description of elementary particles, but we largely lack a mathematical understanding of them. Many efforts have been devoted to the study of the 2D pure Yang-Mills measure, which is now considered well understood. However, the methods used to study this model rely crucially on its integrability and have so far had no extensions to higher dimensions or to more physical models. In this talk, I will present a new approach to QGTs based on stochastic and rough analysis, which has led to new results even for the classical 2D YM measure. I will in particular demonstrate several results that connect QGTs with singular stochastic partial differential equations and rough path theory.