1997/01/10 by В. Б. Кузнецов, V. B. Kuznetsov, Frank Nijhoff +2 · 4 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Computer science #Construct (python library) #Eigenvalues and eigenvectors #Elliptic function #Function (biology) #Generating function #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Nonlinear Waves and Solitons #Partial differential equation #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Separation (statistics) #Separation of variables #Statistics #hep-th #math.QA #nlin.SI #q-alg #solv-int
paper · pdf · doi:10.1007/s002200050231
published as Commun.Math.Phys. 189(1997) 855-877 · 26 pages, LaTex, no figures
arxiv created 1997/01/10 · openalex publication_date 1997/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We construct a separation of variables for the classical n-particle Ruijsenaars system (the relativistic analog of the elliptic Calogero-Moser system). The separated coordinates appear as the poles of the properly normalised eigenvector (Baker-Akhiezer function) of the corresponding Lax matrix. Two different normalisations of the BA functions are analysed. The canonicity of the separated variables is verified with the use of r-matrix technique. The explicit expressions for the generating function of the separating canonical transform are given in the simplest cases n=2 and n=3. Taking nonrelativistic limit we also construct a separation of variables for the elliptic Calogero-Moser system.