Superintegrable systems in non-Euclidean plane: Hidden symmetries leading to linearity
نویسندگان
چکیده
Nineteen classical superintegrable systems in two-dimensional non-Euclidean spaces are shown to possess hidden symmetries leading their linearization. They the two Perlick [A. Ballesteros, A. Enciso, F.J. Herranz and O. Ragnisco, Class. Quantum Grav. 25, 165005 (2008)], Taub-NUT system Herranz, D. Riglioni, SIGMA 7, 048 (2011)], all seventeen for four types of Darboux as determined [E.G. Kalnins, J.M. Kress, W. Miller, P. Winternitz, J. Math. Phys. 44, 5811--5848 (2003)].
منابع مشابه
Hidden symmetries in jammed systems
There are deep, but hidden, geometric structures within jammed systems, associated with hidden symmetries. These can be revealed by repeated transformations under which these structures lead to fixed points. These geometric structures can be found in the Voronoi tesselation of space defined by the packing. In this paper we examine two iterative processes: maximum inscribed sphere (MIS) inversio...
متن کاملSuperintegrable systems with spin in two- and three-dimensional Euclidean spaces
The concept of superintegrability in quantum mechanics is extended to the case of a particle with spin s = 1/2 interacting with one of spin s = 0. Non-trivial superintegrable systems with 8and 9-dimensional Lie algebras of first-order integrals of motion are constructed in twoand three-dimensional spaces, respectively.
متن کاملTopics in Hidden Symmetries
This note being devoted to some aspects of the inverse problem of representation theory contains a new insight into it illustrated by two topics. The attention is concentrated on the manner of representation of abstract objects by the concrete ones as well as on the abstract objects themselves. This paper being a continuation of the previous three parts [1] explicates novel features of the gene...
متن کاملIn Hidden Symmetries . Ii
This short paper being devoted to some aspects of the inverse problem of the representation theory briefly treats the interrelations between the author’s approach to the setting free of hidden symmetries and the researches of D.P.Zhelobenko in the generalized Mickelsson algebras and related topics. This short paper being a continuation of the first part [1] is a collection of examples illustrat...
متن کاملIntegrable and superintegrable systems with spin in three-dimensional Euclidean space
A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spin 0 and 1 2 , is performed. We restrict to integrals of motion that are first-order (matrix) polynomials in the components of linear momentum. Several such systems are found and for one non-trivial example we show how superintegrability leads to exact solvability: we obtain exac...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2021
ISSN: ['0022-2488', '1527-2427', '1089-7658']
DOI: https://doi.org/10.1063/5.0041130