Dirichlet form associated with the ${\Phi }_3^4$ model

Abstract

We construct the Dirichlet form associated with the dynamical ${\Phi }_3^4$ 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 ${\Phi }_3^4$ field measure as an invariant (even symmetrizing) measure.