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

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.