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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], byrestricting the situation where $p =2$, is applied to such measure spaces asthe space cut-off $P(\phi)_2$ Euclidean quantum field, the $2$-dimensionalEuclidean quantum fields with exponential and trigonometric potentials, and thefield describing a system of an infinite number of classical particles. Foreach measure space, the Markov process corresponding to the {\it{non-local}}type stochastic quantization is constructed.

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