A variational method for $\Phi^4_3$

TL;DR

This paper presents a variational approach to defining the $\

Contribution

It introduces a novel variational characterization of the $\

Findings

Explicit description of the $\

Extension of the variational characterization to the unregularized model via $\

Provides a new perspective on the $\

Abstract

We introduce an explicit description of the $\Phi^4_3$ measure on a bounded domain. Our starting point is the interpretation of its Laplace transform as the value function of a stochastic optimal control problem along the flow of a scale regularization parameter. Once small scale singularities have been renormalized by the standard counterterms, $\Gamma$-convergence allows to extend the variational characterization to the unregularized model.