Operator Product Expansions of Derivative Fields in the Sine-Gordon Model

In this article, we initiate the study of operator product expansions (OPEs) for the sine-Gordon model. For simplicity, we focus on the model below the first threshold of collapse ( β <4π β < 4 π ) and on the singular terms in OPEs of derivative-type fields ∂ φ ∂ φ and ∂ ̄φ ∂ ¯ φ . We prove that compared to corresponding free field OPEs, the sine-Gordon OPEs develop logarithmic singularities and generate Wick ordered exponentials. Our approach for proving the OPEs relies heavily on Onsager-type inequalities and associated moment bounds for GFF correlation functions involving Wick ordered exponentials of the free field.