Non-local Markovian symmetric forms on infinite dimensional spaces; Part 2. Examples: non local stochastic quantization of space cut-off quantum fields and infinite particle systems

The general framework on the non-local Markovian symmetric forms on weighted $l^p$ $(p\in [1,\mathrm{\infty }])$ spaces constructed by [A,Kagawa,Yahagi,Y 2020], by restricting the situation where $p=2$, is applied to such measure spaces as the space cut-off $P(\varphi {)}_2$ Euclidean quantum field, the $2$-dimensional Euclidean quantum fields with exponential and trigonometric potentials, and the field describing a system of an infinite number of classical particles. For each measure space, the Markov process corresponding to the {\it{non-local}} type stochastic quantization is constructed.