Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. I. Two-Dimensional Model
A shape-invariant, nonseparable, and nondiagonalizable two-dimensional model with quadratic complex interaction, first studied by Cannata, Ioffe, and Nishnianidze, is re-examined to reveal its hidden algebraic structure. The two operators ⁺ and ⁻, coming from the shape invariant supersymmetrical app...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2022 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2022
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211541 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. I. Two-Dimensional Model. Ian Marquette and Christiane Quesne. SIGMA 18 (2022), 004, 11 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862719541521416192 |
|---|---|
| author | Marquette, Ian Quesne, Christiane |
| author_facet | Marquette, Ian Quesne, Christiane |
| citation_txt | Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. I. Two-Dimensional Model. Ian Marquette and Christiane Quesne. SIGMA 18 (2022), 004, 11 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A shape-invariant, nonseparable, and nondiagonalizable two-dimensional model with quadratic complex interaction, first studied by Cannata, Ioffe, and Nishnianidze, is re-examined to reveal its hidden algebraic structure. The two operators ⁺ and ⁻, coming from the shape invariant supersymmetrical approach, where ⁺ acts as a raising operator. At the same time, ⁻ annihilates all wavefunctions, are completed by introducing a novel pair of operators ⁺ and ⁻, where ⁻ acts as the missing lowering operator. These four operators then serve as building blocks for constructing (2) generators, acting within the set of associated functions belonging to the Jordan block corresponding to a given energy eigenvalue. This analysis is extended to the set of Jordan blocks by constructing two pairs of bosonic operators, finally yielding an (4) algebra, as well as an (1/4) superalgebra. Hence, the hidden algebraic structure of the model is very similar to that known for the two-dimensional real harmonic oscillator.
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| first_indexed | 2026-03-21T00:19:14Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211541 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T00:19:14Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Marquette, Ian Quesne, Christiane 2026-01-05T12:30:30Z 2022 Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. I. Two-Dimensional Model. Ian Marquette and Christiane Quesne. SIGMA 18 (2022), 004, 11 pages 1815-0659 2020 Mathematics Subject Classification: 81Q05; 81Q60; 81R12; 81R15 arXiv:2010.15273 https://nasplib.isofts.kiev.ua/handle/123456789/211541 https://doi.org/10.3842/SIGMA.2022.004 A shape-invariant, nonseparable, and nondiagonalizable two-dimensional model with quadratic complex interaction, first studied by Cannata, Ioffe, and Nishnianidze, is re-examined to reveal its hidden algebraic structure. The two operators ⁺ and ⁻, coming from the shape invariant supersymmetrical approach, where ⁺ acts as a raising operator. At the same time, ⁻ annihilates all wavefunctions, are completed by introducing a novel pair of operators ⁺ and ⁻, where ⁻ acts as the missing lowering operator. These four operators then serve as building blocks for constructing (2) generators, acting within the set of associated functions belonging to the Jordan block corresponding to a given energy eigenvalue. This analysis is extended to the set of Jordan blocks by constructing two pairs of bosonic operators, finally yielding an (4) algebra, as well as an (1/4) superalgebra. Hence, the hidden algebraic structure of the model is very similar to that known for the two-dimensional real harmonic oscillator. I. Marquette was supported by the Australian Research Council Future Fellowship FT180100099. C. Quesne was supported by the Fonds de la Recherche Scientifique- FNRS under Grant Number 4.45.10.08. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. I. Two-Dimensional Model Article published earlier |
| spellingShingle | Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. I. Two-Dimensional Model Marquette, Ian Quesne, Christiane |
| title | Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. I. Two-Dimensional Model |
| title_full | Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. I. Two-Dimensional Model |
| title_fullStr | Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. I. Two-Dimensional Model |
| title_full_unstemmed | Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. I. Two-Dimensional Model |
| title_short | Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. I. Two-Dimensional Model |
| title_sort | ladder operators and hidden algebras for shape invariant nonseparable and nondiagonalizable modelswith quadratic complex interaction. i. two-dimensional model |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211541 |
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