Semiclassical analysis of defect sine-Gordon theory

TL;DR

This paper explores the semiclassical approximation of the defect sine-Gordon theory, comparing classical and quantum results to constrain ambiguities and understand the relation between parameters and spectral resonances.

Contribution

It provides a detailed semiclassical analysis of defect sine-Gordon theory, linking classical and quantum descriptions to reduce CDD ambiguities and analyze spectral features.

Findings

Classical and quantum results are compared to restrict CDD ambiguity.

Relations between classical and quantum parameters are established.

Spectral resonances are analyzed within the semiclassical framework.

Abstract

The classical sine-Gordon model is a two-dimensional integrable field theory, with particle like solutions the so-called solitons. Using its integrability one can define its quantum version without the process of canonical quantization. This bootstrap method uses the fundamental propterties of the model and its quantum features in order to restrict the structure of the scattering matrix as far as possible. The classical model can be extended with integrable discontinuities, purely transmitting jump-defects. Then the quantum version of the extended model can be determined via the bootstrap method again. But the outcoming quantum theory contains the so-called CDD uncertainity. The aim of this article is to carry throw the semiclassical approximation in both the classical and the quantum side of the defect sine-Gordon theory. The CDD ambiguity can be restricted by comparing the two results. The relation between the classical and quantum parameters as well as the resoncances appeared in the spectrum are other objectives.