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

Abstract

We construct the Dirichlet form associated with the dynamical $\Phi ^4_3$ model obtained in [23, 7] and [37]. 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.