A simple construction of the sine-Gordon model via stochastic quantization

TL;DR

This paper introduces a straightforward PDE-based approach to construct the sine-Gordon measure below a certain threshold and proves global well-posedness of the hyperbolic sine-Gordon model in finite volume for specific parameter ranges.

Contribution

It provides a novel PDE construction of the sine-Gordon measure and establishes global well-posedness results for the hyperbolic model.

Findings

Constructed sine-Gordon measure below the first threshold using PDE methods.

Proved pathwise global well-posedness of the hyperbolic sine-Gordon model in finite volume for ^2 < 2.

Analyzed both finite and infinite volume settings for the sine-Gordon model.

Abstract

We present a simple PDE construction of the sine-Gordon measure below the first threshold ($\be^2 < 4\pi$), in both the finite and infinite volume settings, by studying the corresponding parabolic sine-Gordon model. We also establish pathwise global well-posedness of the hyperbolic sine-Gordon model in finite volume for $\be^2 < 2\pi$.