A stochastic control approach to Sine Gordon EQFT

TL;DR

This paper applies stochastic control techniques to analyze the Sine-Gordon quantum field theory in infinite volume, establishing large deviations, correlation decay, and axiomatic properties.

Contribution

It introduces a novel stochastic control framework for the Sine-Gordon model, providing variational characterizations and rigorous proofs of fundamental axioms.

Findings

Large deviations for the Sine-Gordon model

Exponential decay of correlations

Verification of Osterwalder-Schrader axioms

Abstract

We study the Sine-Gordon model for $\beta^{2}< 4 \pi$ in infinite volume. We give a variatonal characterization of it's laplace transform, and deduce from this large deviations. Along the way we obtain estimates which are strong enough to obtain a proof of the Osterwalder-Schrader axioms including exponential decay of correlations as a byproduct. Our method is based on the Boue-Dupuis formula with an emphasis on the stochastic control structure of the problem.