Complex rational Ruijsenaars model. The two-particle case
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917237558870016 |
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| author | Belousov, N. M. Sarkissian, G. A. Spiridonov, V. P. |
| author_facet | Belousov, N. M. Sarkissian, G. A. Spiridonov, V. P. |
| contents | We consider a complex rational degeneration of the hyperbolic Ruijsenaars model emerging in the limit $ω_1+ω_2\to 0$ (or $b\to \imath$ in $2d$ CFT) and investigate in detail the two-particle case. Corresponding wave functions are described by complex hypergeometric functions in the Mellin-Barnes representation. Their dual integral representation and reflection symmetry in the coupling constant are established. Besides, a complex limit of the hyperbolic Baxter $Q$-operators is considered. Another complex degeneration of the hyperbolic Ruijsenaars model is obtained by taking a special $ω_1-ω_2\to 0$ (or $b\to 1$) limit. Additionally, two new degenerations to the complex Calogero-Sutherland type models are described. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12449 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complex rational Ruijsenaars model. The two-particle case Belousov, N. M. Sarkissian, G. A. Spiridonov, V. P. Mathematical Physics High Energy Physics - Theory We consider a complex rational degeneration of the hyperbolic Ruijsenaars model emerging in the limit $ω_1+ω_2\to 0$ (or $b\to \imath$ in $2d$ CFT) and investigate in detail the two-particle case. Corresponding wave functions are described by complex hypergeometric functions in the Mellin-Barnes representation. Their dual integral representation and reflection symmetry in the coupling constant are established. Besides, a complex limit of the hyperbolic Baxter $Q$-operators is considered. Another complex degeneration of the hyperbolic Ruijsenaars model is obtained by taking a special $ω_1-ω_2\to 0$ (or $b\to 1$) limit. Additionally, two new degenerations to the complex Calogero-Sutherland type models are described. |
| title | Complex rational Ruijsenaars model. The two-particle case |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2508.12449 |