Stochastic quantization and Osterwalder-Schrader axioms for quantum field theory models

This PhD thesis constructs the $P(Φ)_2$ Euclidean quantum field theory on $\mathscr{S}'(\mathbb{R}^2)$. We first construct the finite-volume measure of the $P(Φ)_2$ model on $\mathscr{D}'(\mathbb{S}_R)$, where $\mathbb{S}_R$ is a two-dimensional sphere of radius $R\in\mathbb{N}_+$. To this end, we r