Quantization of Calogero-Painlevé System and Multi-Particle Quantum Painlevé Equations II-VI
We consider the isomonodromic formulation of the Calogero-Painlevé multi-particle systems and proceed to their canonical quantization. We then proceed to the quantum Hamiltonian reduction on a special representation to radial variables, in analogy with the classical case and also with the theory of...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2021 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211446 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Quantization of Calogero-Painlevé System and Multi-Particle Quantum Painlevé Equations II-VI. Fatane Mobasheramini and Marco Bertola. SIGMA 17 (2021), 081, 25 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862698423136813056 |
|---|---|
| author | Mobasheramini, Fatane Bertola, Marco |
| author_facet | Mobasheramini, Fatane Bertola, Marco |
| citation_txt | Quantization of Calogero-Painlevé System and Multi-Particle Quantum Painlevé Equations II-VI. Fatane Mobasheramini and Marco Bertola. SIGMA 17 (2021), 081, 25 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider the isomonodromic formulation of the Calogero-Painlevé multi-particle systems and proceed to their canonical quantization. We then proceed to the quantum Hamiltonian reduction on a special representation to radial variables, in analogy with the classical case and also with the theory of quantum Calogero equations. This quantized version is compared to the generalization of a result of Nagoya on integral representations of certain solutions of the quantum Painlevé equations. We also provide multi-particle generalizations of these integral representations.
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| first_indexed | 2026-03-18T10:20:09Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211446 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-18T10:20:09Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Mobasheramini, Fatane Bertola, Marco 2026-01-02T08:36:02Z 2021 Quantization of Calogero-Painlevé System and Multi-Particle Quantum Painlevé Equations II-VI. Fatane Mobasheramini and Marco Bertola. SIGMA 17 (2021), 081, 25 pages 1815-0659 2020 Mathematics Subject Classification: 70H08; 81R12 arXiv:2103.09681 https://nasplib.isofts.kiev.ua/handle/123456789/211446 https://doi.org/10.3842/SIGMA.2021.081 We consider the isomonodromic formulation of the Calogero-Painlevé multi-particle systems and proceed to their canonical quantization. We then proceed to the quantum Hamiltonian reduction on a special representation to radial variables, in analogy with the classical case and also with the theory of quantum Calogero equations. This quantized version is compared to the generalization of a result of Nagoya on integral representations of certain solutions of the quantum Painlevé equations. We also provide multi-particle generalizations of these integral representations. The work of F.M. and M.B. was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) grant RGPIN-2016-06660. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quantization of Calogero-Painlevé System and Multi-Particle Quantum Painlevé Equations II-VI Article published earlier |
| spellingShingle | Quantization of Calogero-Painlevé System and Multi-Particle Quantum Painlevé Equations II-VI Mobasheramini, Fatane Bertola, Marco |
| title | Quantization of Calogero-Painlevé System and Multi-Particle Quantum Painlevé Equations II-VI |
| title_full | Quantization of Calogero-Painlevé System and Multi-Particle Quantum Painlevé Equations II-VI |
| title_fullStr | Quantization of Calogero-Painlevé System and Multi-Particle Quantum Painlevé Equations II-VI |
| title_full_unstemmed | Quantization of Calogero-Painlevé System and Multi-Particle Quantum Painlevé Equations II-VI |
| title_short | Quantization of Calogero-Painlevé System and Multi-Particle Quantum Painlevé Equations II-VI |
| title_sort | quantization of calogero-painlevé system and multi-particle quantum painlevé equations ii-vi |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211446 |
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