Dirichlet form associated with the $\Phi_3^4$ model

TL;DR

This paper constructs and analyzes the Dirichlet form linked to the dynamical $\

Contribution

It establishes the classical gradient bilinear form as a closable and quasi-regular Dirichlet form for the $\

Findings

The Dirichlet form is identified as a classical gradient bilinear form.

The form is shown to be closable and quasi-regular.

Existence of a Markov diffusion process with $\

Abstract

We construct the Dirichlet form associated with the dynamical $\Phi^4_3$ model obtained in [Hai14, CC13] and [MW16]. This Dirichlet form on cylinder functions is identified as a classical gradient bilinear form. As a consequence, this classical gradient bilinear form is closable and then by a well-known result its closure is also a quasi-regular Dirichlet form, which means that there exists another (Markov) diffusion process, which also admits the $\Phi^4_3$ field measure as an invariant (even symmetrizing) measure.