Dynamical symmetries of the Calogero-Coulomb model
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917544825192448 |
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| author | Hakobyan, Tigran |
| author_facet | Hakobyan, Tigran |
| contents | We construct the dynamical symmetry of the quantum Calogero model with particle exchange in a confining Coulomb field. This symmetry is governed by the algebra $so(N+1,2)$, deformed by exchange (Dunkl) operators, with its invariant sector generated by the Dunkl angular momentum tensor and the modified Laplace-Runge-Lenz vector. The equidistant analogue of the Hamiltonian, with a linear spectrum, is expressed in terms of the conformal subalgebra $so(1,2)$. In addition, the wave functions of the Calogero-Coulomb Hamiltonian are classified into infinite-dimensional lowest-weight $so(1,2)$ multiplets. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_21325 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dynamical symmetries of the Calogero-Coulomb model Hakobyan, Tigran High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems Quantum Physics We construct the dynamical symmetry of the quantum Calogero model with particle exchange in a confining Coulomb field. This symmetry is governed by the algebra $so(N+1,2)$, deformed by exchange (Dunkl) operators, with its invariant sector generated by the Dunkl angular momentum tensor and the modified Laplace-Runge-Lenz vector. The equidistant analogue of the Hamiltonian, with a linear spectrum, is expressed in terms of the conformal subalgebra $so(1,2)$. In addition, the wave functions of the Calogero-Coulomb Hamiltonian are classified into infinite-dimensional lowest-weight $so(1,2)$ multiplets. |
| title | Dynamical symmetries of the Calogero-Coulomb model |
| topic | High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems Quantum Physics |
| url | https://arxiv.org/abs/2603.21325 |