Perturbation theory in radial quantization approach and the expectation values of exponential fields in sine-Gordon model

TL;DR

This paper develops a perturbation theory in radial quantization for the Massive Thirring Model, enabling calculation of exponential field expectation values in sine-Gordon theory, confirming conjectured formulas and overcoming quantization difficulties.

Contribution

It introduces a novel perturbation approach in radial quantization for massive theories, allowing explicit expectation value calculations in sine-Gordon model.

Findings

Agreement with Lukyanov and Zamolodchikov's conjectured formulas

Successful handling of explicit time dependence in radial quantization

Consistency with dual angular quantization results

Abstract

A perturbation theory for Massive Thirring Model (MTM) in radial quantization approach is developed. Investigation of the twisted sector in this theory allows us to calculate the vacuum expectation values of exponential fields $ exp iaphi (0) $ of the sine-Gordon theory in first order over Massive Thirring Models coupling constant. It appears that the apparent difficulty in radial quantization of massive theories, namely the explicite ''time'' dependence of the Hamiltonian, may be successfully overcome. The result we have obtained agrees with the exact formula conjectured by Lukyanov and Zamolodchikov and coincides with the analogous calculations recently carried out in dual angular quantization approach by one of the authors.