Shyuji Kawasaki | Searcharxiv

arXiv2023

A general formulation of Non-Local Dirichlet forms on infinite dimensional topological vector spaces and its applications, and corresponding subjects: Seminar at Univ. Lisboa,2023

A concise explanations on the results given by Non-local Markovian Symmetric Forms on Infinite Dimensional Spaces I, CMP 2021, by Sergio Albeverio, Minoru W. Yoshida, et.al., and Non-local Markovian Symmetric Forms on Infinite Dimensional Spaces Part 2, Potential Analysis 2022, by Sergio Albeverio, Minoru W. Yoshida, et.al.are given as a digestive fashion.

math.FA↗

arXiv2021

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 $l^p$ $(p \in [1, \infty])$ 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 $P(ϕ)_2$ 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.

math-ph↗