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

A stochastic control approach to Sine Gordon EQFT