Non-local Markovian Symmetric Forms on Infinite Dimensional Spaces

The general framework on the non-local Markovian symmetric forms on weighted lp $(p \in [1, \infty ])$ spaces constructed by Albeverio et al. (Commn. Math. Phys. 388, 659–706, 2021 Kagawa) by restricting the situation where p = 2, is applied to probability measure spaces describing the space cut-off P(ϕ)2 Euclidean quantum field, the 2-dimensional Euclidean quantum fields with exponential and trigonometric potentials, and the measure associated with the field describing a system of an infinite number of classical particles. For each measure space, the Markov process corresponding to the non-local type stochastic quantization is constructed.