  The general framework on the non-local Markovian symmetric forms on weighted
$l^p$ $(p \in [1, \infty])$ 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 $P(\phi)_2$ 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.
