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

TL;DR

This paper extends the framework of non-local Markovian symmetric forms to infinite-dimensional spaces, applying it to quantum field models and particle systems, and constructs associated non-local stochastic quantization processes.

Contribution

It introduces new examples of non-local stochastic quantization for quantum fields and particle systems within an extended theoretical framework.

Findings

Constructed Markov processes for non-local stochastic quantization

Applied framework to quantum field models with various potentials

Extended the theory to infinite particle systems

Abstract

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.