Sine-Gordon Expectation Values of Exponential Fields With Variational Perturbation Theory

TL;DR

This paper employs variational perturbation theory to compute expectation values of exponential fields in the 2D sine-Gordon model, achieving good agreement with known exact results for small parameters.

Contribution

It introduces a second-order variational perturbation method to evaluate exponential field expectation values in the sine-Gordon model, providing a numerical approach aligned with conjectured exact formulas.

Findings

Results agree well with the exact formula for small parameter values.

Second-order variational perturbation yields accurate expectation values.

Method offers a practical alternative for complex quantum field calculations.

Abstract

In this paper, expectation values of exponential fields in the 2-dimensional Euclidean sine-Gordon field theory are calculated with variational perturbation approach up to the second order. Our numerical analysis indicates that for not large values of the exponential-field parameter $a$, our results agree very well with the exact formula conjectured by Lukyanov and Zamolodchikov in Nucl. Phys. B 493, 571 (1997).