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A variational method for $\Phi^4_3$
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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.
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Cited by 1 Pith paper
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An FBSDE Construction of the Sine-Gordon EQFT for $\beta^{2} < \frac{6}{7}\, 8\pi$ and Perturbative Renormalization in the Full Subcritical Regime
The 2D finite-volume sine-Gordon measure is constructed for β² < (6/7)·8π via a weak FBSDE/control problem, with an order-by-order renormalization-flow analysis valid for all β² < 8π.
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