Elliptic stochastic quantization of Sinh-Gordon QFT

Abstract

The (elliptic) stochastic quantization equation for the (massive) $\cosh ({\hat{I}}^2\ddot{I}†{)}_2$ 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 $\cosh ({\hat{I}}^2\ddot{I}†{)}_2$ quantum field theory, including the exponential decay of correlation functions.

Some typos and erros have been corrected. This version has been accepted for publication in "Stochastics and Partial Differential Equations: Analysis and Computations"