Elliptic stochastic quantization of Sinh-Gordon QFT

TL;DR

This paper investigates the elliptic stochastic quantization of the sinh-Gordon quantum field theory, establishing existence, uniqueness, and properties of solutions, and verifying axioms for the quantum field through lattice approximations and Besov space analysis.

Contribution

It introduces a novel approach to stochastic quantization of sinh-Gordon QFT, proving key properties and connecting the equation to quantum field axioms.

Findings

Existence and uniqueness of solutions to the stochastic quantization equation.

Verification of Osterwalder-Schrader axioms for the quantum field.

Establishment of exponential decay of correlation functions.

Abstract

The (elliptic) stochastic quantization equation for the (massive) $\cosh(\beta \varphi)_2$ model, for the charged parameter in the $L^2$ regime (i.e. $\beta^2 < 4 \pi$), 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 $\cosh (\beta \varphi)_2$ quantum field theory, including the exponential decay of correlation functions.