Two-body Coulomb problem and hidden $g^{(2)}$ algebra: superintegrability and cubic polynomial algebra
| Autor: | Turbiner, Alexander V., Escobar-Ruiz, Adrian M. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | J.Phys.: Conference Series, 2667 (2023) 012075 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1742-6596/2667/1/012075 |
| Popis: | It is shown that the two-body Coulomb problem in the Sturm representation leads to a new two-dimensional, exactly-solvable, superintegrable quantum system in curved space with a $g^{(2)}$ hidden algebra and a cubic polynomial algebra of integrals. The two integrals are of orders two and four, they are made from two components of the angular momentum and from the modified Laplace-Runge-Lenz vector, respectively. It is demonstrated that the cubic polynomial algebra is an infinite-dimensional subalgebra of the universal enveloping algebra $U_{g^{(2)}}$. Comment: 7 pages |
| Databáze: | arXiv |
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