On the Yang-Baxter Poisson algebra in non-ultralocal integrable systems

TL;DR

This paper investigates the emergence of the Yang-Baxter Poisson algebra in non-ultralocal integrable systems, especially those related to deformations of the Principal Chiral Field, addressing challenges in their quantization.

Contribution

It provides new insights into how the Yang-Baxter Poisson algebra appears in non-ultralocal models, which are difficult to analyze with existing methods.

Findings

Identifies conditions for the Yang-Baxter Poisson algebra in non-ultralocal systems

Connects algebra emergence to integrable deformations of the Principal Chiral Field

Offers a framework for understanding quantization of non-ultralocal models

Abstract

A common approach to the quantization of integrable models starts with the formal substitution of the Yang-Baxter Poisson algebra with its quantum version. However it is difficult to discern the presence of such an algebra for the so-called non-ultralocal models. The latter includes the class of non-linear sigma models which are most interesting from the point of view of applications. In this work, we investigate the emergence of the Yang-Baxter Poisson algebra in a non-ultralocal system which is related to integrable deformations of the Principal Chiral Field.