Hamiltonian integrable systems in a magnetic field and Symplectic-Haantjes geometry
Mathematical Physics
2024-11-07 v2 Differential Geometry
math.MP
Exactly Solvable and Integrable Systems
Abstract
We investigate the geometry of classical Hamiltonian systems immersed in a magnetic field in three-dimensional Riemannian configuration spaces. We prove that these systems admit non-trivial symplectic-Haantjes manifolds, which are symplectic manifolds endowed with an algebra of Haantjes (1,1)-tensors. These geometric structures allow us to determine separation variables for known systems algorithmically; besides, the underlying St\"ackel geometry is used to construct new families of integrable Hamiltonian models immersed in a magnetic field.
Keywords
Cite
@article{arxiv.2401.16897,
title = {Hamiltonian integrable systems in a magnetic field and Symplectic-Haantjes geometry},
author = {Ondřej Kubů and Daniel Reyes and Piergiulio Tempesta and Giorgio Tondo},
journal= {arXiv preprint arXiv:2401.16897},
year = {2024}
}
Comments
25 pages, no figures. Includes minor revisions enhancing clarity suggested by referees for Proceedings of Royal Society A and some additional comments