Hamiltonian integrable systems in a magnetic field and Symplectic-Haantjes geometry

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 Stäckel geometry is used to construct new families of integrable Hamiltonian models immersed in a magnetic field.

25 pages, no figures. Includes minor revisions enhancing clarity suggested by referees for Proceedings of Royal Society A and some additional comments

References in corpus (5)

• Integrable and superintegrable quantum systems in a magnetic field
• New classes of quadratically integrable systems in magnetic fields: the generalized cylindrical and spherical cases
• New classes of quadratically integrable systems with velocity dependent potentials: non-subgroup type cases
• Partial separability and symplectic-Haantjes manifolds
• Integrable systems in magnetic fields: the generalized parabolic cylindrical case