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

被引：0
作者：
Kubu, Ondrej [1 ]
Reyes, Daniel [2 ,3 ]
Tempesta, Piergiulio [2 ,3 ]
Tondo, Giorgio [4 ]
机构：
[1] Czech Tech Univ, Fac Nucl Sci & Phys Engn, Dept Phys, Prague, Czech Republic
[2] Inst Ciencias Matemat ICMAT, C Nicolas Cabrera 13-15, Madrid 28049, Spain
[3] Univ Complutense Madrid, Fac Ciencias Fis, Dept Fis Teor, Madrid 28040, Spain
[4] Univ Trieste, Dipartimento Matemat Informat & Geosci, Trieste, Italy
来源：
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2024年 / 480卷 / 2301期
关键词：
integrable systems; Haantjes geometry; magnetic systems; St & auml; ckel systems; SEPARATION; VARIABLES;
D O I：
10.1098/rspa.2024.0076
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
We investigate the geometry of classical Hamiltonian systems immersed in a magnetic field in three-dimensional (3D) 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. In addition, the underlying St & auml;ckel geometry is used to construct new families of integrable Hamiltonian models immersed in a magnetic field.
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页数：24
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