2018/01/31 by A. Grekov, A. Zotov · 18 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Dimension (graph theory) #Integrable system #Lax pair #Mathematical physics #Mathematics #Matrix (chemical analysis) #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum #Quantum mechanics #R-matrix #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1088/1751-8121/aac7b6
published in Journal of Physics A Mathematical and Theoretical 51(31), 315202 (Institute of Physics) · 28 pages, minor corrections
openalex created_date 2018/01/12 · arxiv created 2018/05/19 · openalex publication_date 2018/05/24 · arxiv updated 2018/06/26 · openalex updated_date 2026/08/06
Abstract This article is devoted to the study of R -matrix-valued Lax pairs for N -body (elliptic) Calogero–Moser models. Their matrix elements are given by quantum R -matrices of Baxter–Belavin type. For the widely known Krichever’s Lax pair with spectral parameter is reproduced. First, we construct the R -matrix-valued Lax pairs for Calogero–Moser models associated with classical root systems. For this purpose we study generalizations of the D’Hoker–Phong Lax pairs. It appeared that in the R -matrix-valued case the Lax pairs exist in special cases only. The number of quantum spaces (on which R -matrices act) and their dimension depend on the values of coupling constants. Some of the obtained classical Lax pairs admit straightforward extension to the quantum case. In the end we describe a relationship of the R -matrix-valued Lax pairs to Hitchin systems defined on bundles with nontrivial characteristic classes over elliptic curve. We show that the classical analogue of the anisotropic spin exchange operator entering the R -matrix-valued Lax equations is reproduced in these models.