1998/05/08 by Ángel Ballesteros, Angel Ballesteros, Ballesteros, Angel +2
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Quantum Algebra (math.QA) #math.QA #nlin.SI #solv-int
paper · pdf · doi:10.48550/arxiv.solv-int/9805004
17 pages, LaTeX
arxiv created 1998/05/08 · openalex publication_date 1998/05/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Completely integrable Hamiltonians defining classical mechanical systems of N coupled oscillators are obtained from Poisson realizations of Heisenberg--Weyl, harmonic oscillator and sl(2,\R) coalgebras. Various completely integrable deformations of such systems are constructed by considering quantum deformations of these algebras. Explicit expressions for all the deformed Hamiltonians and constants of motion are given, and the long-range nature of the interactions is shown to be linked to the underlying coalgebra structure. The relationship between oscillator systems induced from the sl(2,\R) coalgebra and angular momentum chains is presented, and a non-standard integrable deformation of the hyperbolic Gaudin system is obtained.