Perturbation Theory in Angular Quantization Approach and the Expectation Values of Exponential Fields in Sin-Gordon Model

TL;DR

This paper develops a perturbation theory within the angular quantization framework to compute vacuum expectation values of exponential fields in the sine-Gordon model, aligning with conjectured exact formulas.

Contribution

It introduces a perturbation approach in angular quantization for the sine-Gordon model that confirms the conjectured exact expressions for expectation values.

Findings

Perturbation theory matches conjectured exact formulas.

Hankel transforms are crucial in calculations.

Results are valid near the free fermion point.

Abstract

In angular quantization approach a perturbation theory for the Massive Thirring Model (MTM) is developed, which allows us to calculate Vacuum Expectation Values of exponential fields in sin-Gordon theory near the free fermion point in first order of MTM coupling constant $g$. The Hankel-transforms play an important role when carrying out this calculations. The expression we have found coincides with that of the direct expansion over $g$ of the exact formula conjectured by S.Lukyanov and A.Zamolodchikov.