An Infinite Family of Maximally Superintegrable Systems in a Magnetic Field with Higher Order Integrals

被引：14

作者：

Marchesiello, Antonella ^{[1
]}

Snobl, Libor ^{[2
]}

机构：

[1] Czech Tech Univ, Fac Informat Technol, Dept Appl Math, Thakurova 9, Prague 16000 6, Czech Republic

[2] Czech Tech Univ, Fac Nucl Sci & Phys Engn, Dept Phys, Brehova 7, Prague 11519 1, Czech Republic

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2018年 / 14卷

关键词：

integrability; superintegrability; higher order integrals; magnetic field; VELOCITY-DEPENDENT POTENTIALS; HAMILTONIAN-SYSTEMS; VECTOR POTENTIALS; DEGENERACY; OSCILLATOR; SYMMETRIES; MECHANICS; MONOPOLE; MOTION;

D O I：

10.3842/SIGMA.2018.092

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct an additional independent integral of motion for a class of three dimensional minimally superintegrable systems with constant magnetic field. This class was introduced in [J. Phys. A: Math. Theor. 50 (2017), 245202, 24 pages] and it is known to possess periodic closed orbits. In the present paper we demonstrate that it is maximally superintegrable. Depending on the values of the parameters of the system, the newly found integral can be of arbitrarily high polynomial order in momenta.

引用

页数：11

共 28 条

[1]

[Anonymous], 1997, Classical Mathematical Physics. Dynamical Systems and Field Theories

[2]

Bagrov V.G., 1972, Sov. Phys. J, V15, P1115

[3] Variable separation for natural Hamiltonians with scalar and vector potentials on Riemannian manifolds [J].