(3) Polynomial Integrable System: Different Faces of the 3-Body/₂ Elliptic Calogero Model

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Authors: Turbiner, Alexander V., Lopez Vieyra, Juan Carlos, Guadarrama-Ayala, Miguel A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212111
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: (3) Polynomial Integrable System: Different Faces of the 3-Body/₂ Elliptic Calogero Model. Alexander V. Turbiner, Juan Carlos Lopez Vieyra and Miguel A. Guadarrama-Ayala. SIGMA 20 (2024), 012, 23 pages

It is shown that the (3) polynomial integrable system, introduced by Sokolov-Turbiner in [J. Phys. A 48 (2015), 155201, 15 pages, arXiv:1409.7439], is equivalent to the (3) quantum Euler-Arnold top in a constant magnetic field. Their Hamiltonian and third-order integral can be rewritten in terms of...