Hidden local, quasi-local and non-local Symmetries in Integrable Systems

TL;DR

This paper develops a framework for discovering and analyzing hidden, quasi-local, and non-local symmetries in classical integrable systems, with implications for understanding quantum models and their spectra.

Contribution

It introduces a general approach to identify and study various symmetries in integrable systems, unifying perspectives on KdV hierarchies and Toda theories.

Findings

Virasoro algebra as symmetry of Sine-Gordon model

Unified view of KdV and Toda symmetries

Enhanced understanding of conserved quantities

Abstract

The knowledge of {\it non usual} and sometimes {\it hidden} symmetries of (classical) integrable systems provides a very powerful setting-out of solutions of these models. Primarily, the understanding and possibly the quantisation of intriguing symmetries could give rise to deeper insight into the nature of field spectrum and correlation functions in quantum integrable models. With this perspective in mind we will propose a general framework for discovery and investigation of local, quasi-local and non-local symmetries in classical integrable systems. We will pay particular attention to the structure of symmetry algebra and to the r\^ole of conserved quantities. We will also stress a nice unifying point of view about KdV hierarchies and Toda field theories with the result of obtaining a Virasoro algebra as exact symmetry of Sine-Gordon Model.