Ergodicity for the stochastic quantization problems on the 2D-torus

TL;DR

This paper investigates the ergodic behavior of solutions to stochastic quantization equations on the 2D torus and characterizes the $\

Contribution

It establishes ergodicity for stochastic quantization on the 2D torus and characterizes the $\

Findings

Proves ergodicity of solutions.

Characterizes the $\

The $\

Abstract

In this paper we study the stochastic quantization problem on the two dimensional torus and establish ergodicity for the solutions. Furthermore, we prove a characterization of the $\Phi^4_2$ quantum field on the torus in terms of its density under translation. We also deduce that the $\Phi^4_2$ quantum field on the torus is an extreme point in the set of all $L$-symmetrizing measures, where $L$ is the corresponding generator.