A simple construction of the sine-Gordon model via stochastic quantization

We present a simple PDE construction of the sine-Gordon measure below the first threshold (${\text{be}}^2<4\pi$), in both the finite and infinite volume settings, by studying the corresponding parabolic sine-Gordon model. We also establish pathwise global well-posedness of the hyperbolic sine-Gordon model in finite volume for ${\text{be}}^2<2\pi$.