Dirichlet form associated with the $Φ_3^4$ model

Rongchan Zhu, Xiangchan Zhu

Published 2017-03-29Version 1

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.