A superintegrable model with reflections on $S^3$ and the rank two Bannai-Ito algebra
| Autor: | Hendrik De Bie, Vincent X. Genest, Jean-Michel Lemay, Luc Vinet |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Cauchy-Kovalevskaia extension
Pure mathematics Current algebra FOS: Physical sciences 01 natural sciences Filtered algebra symbols.namesake Bannai-Ito algebra 0103 physical sciences Superintegrable Hamiltonian system 0101 mathematics quantum superintegrable model Mathematical Physics Mathematics 010308 nuclear & particles physics 010102 general mathematics General Engineering Quantum algebra Mathematical Physics (math-ph) Superalgebra Algebra Tensor product Mathematics and Statistics Nonlinear Sciences::Exactly Solvable and Integrable Systems lcsh:TA1-2040 symbols Cellular algebra lcsh:Engineering (General). Civil engineering (General) Hamiltonian (quantum mechanics) |
| Zdroj: | ACTA POLYTECHNICA Acta Polytechnica, Vol 56, Iss 3, Pp 166-172 (2016) |
| ISSN: | 1210-2709 1805-2363 |
| Popis: | A quantum superintegrable model with reflections on the three-sphere is presented. Its symmetry algebra is identified with the rank-two Bannai-Ito algebra. It is shown that the Hamiltonian of the system can be constructed from the tensor product of four representations of the superalgebra $\mathfrak{osp}(1|2)$ and that the superintegrability is naturally understood in that setting. The exact separated solutions are obtained through the Fischer decomposition and a Cauchy-Kovalevskaia extension theorem. 8 pages |
| Databáze: | OpenAIRE |
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