Elliptic stochastic quantization of Sinh-Gordon QFT
Abstract
The (elliptic) stochastic quantization equation for the (massive) model, for the charged parameter in the regime (i.e. ), 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 quantum field theory, including the exponential decay of correlation functions.
Cite
@article{arxiv.2108.12664,
title = {Elliptic stochastic quantization of Sinh-Gordon QFT},
author = {Nikolay Barashkov and Francesco C. De Vecchi},
journal= {arXiv preprint arXiv:2108.12664},
year = {2025}
}
Comments
Some typos and erros have been corrected. This version has been accepted for publication in "Stochastics and Partial Differential Equations: Analysis and Computations"