English

Elliptic stochastic quantization of Sinh-Gordon QFT

Probability 2025-06-18 v3 Mathematical Physics Analysis of PDEs math.MP

Abstract

The (elliptic) stochastic quantization equation for the (massive) cosh(βφ)2\cosh(\beta \varphi)_2 model, for the charged parameter in the L2L^2 regime (i.e. β2<4π\beta^2 < 4 \pi), 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(βφ)2\cosh (\beta \varphi)_2 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"

R2 v1 2026-06-24T05:29:38.499Z