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.

29 pages, 2 figures. v3: stylistic improvements - formulae simplified, Appendix A integrated into the main text

References in corpus (3)

• On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
• Generalised integrable $\lambda$- and $\eta$-deformations and their relation
• On the Hamiltonian integrability of the bi-Yang-Baxter sigma-model

Cited by in corpus (10)

• Scaling limit of the ${\mathcal{Z}}_2$ invariant inhomogeneous six-vertex model
• Dressing cosets and multi-parametric integrable deformations
• Strong integrability of the bi-YB-WZ model
• Affine Poisson and affine quasi-Poisson T-duality
• An elliptic integrable deformation of the Principal Chiral Model
• Non-ultralocal classical r-matrix structure for 1+1 field analogue of elliptic Calogero-Moser model
• On a class of conformal $\mathcal{E}$-models and their chiral Poisson algebras
• Integrability and renormalizability for the fully anisotropic $\mathrm{SU}(2)$ principal chiral field and its deformations
• On the Integrable Structure of the SU(2) Wess-Zumino-Novikov-Witten Model
• Nonperturbative features in the Lie-algebraic Kähler sigma model with fermions