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Elliptic stochastic quantization of Sinh-Gordon QFT
Nikolay Barashkov, Francesco C. De Vecchi · 2021-08-28 · via math.PR updates on arXiv.org

The (elliptic) stochastic quantization equation for the (massive) $\cosh(β\varphi)_2$ model, for the charged parameter in the $L^2$ regime (i.e. $β^2 < 4 π$), is studied. We prove the existence, uniqueness and the properties of the invariant measure of the solution to this equation. The proof is obtained through a priori estimates and a lattice approximation of the equation. For implementing this strategy we generalize some properties of Besov spaces in the continuum to analogous results for Besov spaces on the lattice. As a final result we show how to use the stochastic quantization equation to verify the Osterwalder-Schrader axioms for the $\cosh (β\varphi)_2$ quantum field theory, including the exponential decay of correlation functions.

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