Strong uniqueness for certain infinite dimensional Dirichlet operators and applications to stochastic quantization
Vitali Liskevich and Michael Röckner
Strong and Markov uniqueness problems in $L^2$ for Dirichlet operators on rigged Hilbert spaces are studied. An analytic approach based on a priori estimates is used. The extension of the problem to the $L^p$-setting is discussed. As a direct application essential self–adjointness and strong uniqueness in $L^p$ is proved for the generator (with initial domain the bounded smooth cylinder functions) of the stochastic quantization process for Euclidean quantum field theory in finite volume $\Lambda \subset {\mathbb R}^2$.