How SPDEs may be used to construct Euclidean QFTs
In this talk, we will give a brief introduction to the method of stochastic quantization. We will begin with a short review of euclidean Quantum Field Theories (eQFT), which are given by probability measures over distribution spaces. The method of stochastic quantization is a dynamical approach to constructing these probability measures. Namely, one constructs a particular set of dynamics whose stationary measure is given by the eQFT. In the cases we will be interested in, these dynamics correspond to solutions of stochastic partial differential equations (SPDEs). We will sketch out a rough blueprint of how one constructs solutions to these SPDEs and run through some examples. Minimal probability background will be assumed.