Coupling and particle number intertwiners in the Calogero model
Abstract It is long known that quantum Calogero models feature intertwining operators, which increase or decrease the coupling constant by an integer amount, for any fixed number of particles. We name these as “horizontal” and construct “vertical” intertwiners, which change the number of interacting...
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SpringerOpen
2025-07-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP07(2025)128 |
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| author | Francisco Correa Luis Inzunza Olaf Lechtenfeld |
| author_facet | Francisco Correa Luis Inzunza Olaf Lechtenfeld |
| author_sort | Francisco Correa |
| collection | DOAJ |
| description | Abstract It is long known that quantum Calogero models feature intertwining operators, which increase or decrease the coupling constant by an integer amount, for any fixed number of particles. We name these as “horizontal” and construct “vertical” intertwiners, which change the number of interacting particles for a fixed but integer value of the coupling constant. The emerging structure of a grid of intertwiners exists only in the algebraically integrable situation (integer coupling) and allows one to obtain each Liouville charge from the free power sum in the particle momenta by iterated intertwining either horizontally or vertically. We present recursion formulæ for the intertwiners as a factorization problem for partial differential operators and prove their existence for small values of particle number and coupling. As a byproduct, a new basis of non-symmetric Liouville integrals appears, algebraically related to the standard symmetric one. |
| format | Article |
| id | doaj-art-50a6d8541ac14c6285b3fde22b5b700c |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-50a6d8541ac14c6285b3fde22b5b700c2025-08-20T04:01:42ZengSpringerOpenJournal of High Energy Physics1029-84792025-07-012025712110.1007/JHEP07(2025)128Coupling and particle number intertwiners in the Calogero modelFrancisco Correa0Luis Inzunza1Olaf Lechtenfeld2Departamento de Física, Universidad de Santiago de ChileDepartamento de Física, Universidad de Santiago de ChileInstitut für Theoretische Physik and Riemann Center for Geometry and Physics, Leibniz Universität HannoverAbstract It is long known that quantum Calogero models feature intertwining operators, which increase or decrease the coupling constant by an integer amount, for any fixed number of particles. We name these as “horizontal” and construct “vertical” intertwiners, which change the number of interacting particles for a fixed but integer value of the coupling constant. The emerging structure of a grid of intertwiners exists only in the algebraically integrable situation (integer coupling) and allows one to obtain each Liouville charge from the free power sum in the particle momenta by iterated intertwining either horizontally or vertically. We present recursion formulæ for the intertwiners as a factorization problem for partial differential operators and prove their existence for small values of particle number and coupling. As a byproduct, a new basis of non-symmetric Liouville integrals appears, algebraically related to the standard symmetric one.https://doi.org/10.1007/JHEP07(2025)128Integrable HierarchiesConformal and W SymmetryDiscrete SymmetriesIntegrable Field Theories |
| spellingShingle | Francisco Correa Luis Inzunza Olaf Lechtenfeld Coupling and particle number intertwiners in the Calogero model Journal of High Energy Physics Integrable Hierarchies Conformal and W Symmetry Discrete Symmetries Integrable Field Theories |
| title | Coupling and particle number intertwiners in the Calogero model |
| title_full | Coupling and particle number intertwiners in the Calogero model |
| title_fullStr | Coupling and particle number intertwiners in the Calogero model |
| title_full_unstemmed | Coupling and particle number intertwiners in the Calogero model |
| title_short | Coupling and particle number intertwiners in the Calogero model |
| title_sort | coupling and particle number intertwiners in the calogero model |
| topic | Integrable Hierarchies Conformal and W Symmetry Discrete Symmetries Integrable Field Theories |
| url | https://doi.org/10.1007/JHEP07(2025)128 |
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