2018/05/31 by Vladimir V. Bazhanov, Gleb A. Kotousov, Sergei L. Lukyanov
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Chiral model #Field (mathematics) #Integrable system #Lie algebra #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Nonlinear system #Physics #Poisson algebra #Poisson bracket #Poisson distribution #Pure mathematics #Quantization (signal processing) #Quantum mechanics #Sigma model #Statistics #hep-th #math-ph #math.MP
paper · pdf · doi:10.1016/j.nuclphysb.2018.07.016
29 pages, 2 figures. v3: stylistic improvements - formulae simplified, Appendix A integrated into the main text
openalex publication_date 2018/07/20 · arxiv created 2022/03/07 · arxiv updated 2022/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.