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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.09568 |
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| _version_ | 1866915687505592320 |
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| author | Antonenko, Pavel V. Derkachov, Sergey É. Valinevich, Pavel A. |
| author_facet | Antonenko, Pavel V. Derkachov, Sergey É. Valinevich, Pavel A. |
| contents | For the noncompact open ${\rm SL}(2,\mathbb{C})$ spin chain, the eigenfunctions of the special matrix element of monodromy matrix are constructed. The key ingredients of the whole construction are local Yang-Baxter $\mathcal{R}$-operators, $Q$-operator and raising operators obtained by reduction from the $Q$-operator. The calculation of various scalar products and the proof of orthogonality are based on the properties of $Q$-operator and demonstrate its hidden role. The symmetry of eigenfunctions with respect to reflection of the spin variable $s \to 1-s$ is established. The Mellin-Barnes representation for eigenfunctions is derived and equivalence with initial coordinate representation is proved. The transformation from one representation to another is grounded on the application of $A$-type Gustafson integral generalized to the complex field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09568 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A-Type Open ${\rm SL}(2,\mathbb{C})$ Spin Chain Antonenko, Pavel V. Derkachov, Sergey É. Valinevich, Pavel A. High Energy Physics - Theory Mathematical Physics For the noncompact open ${\rm SL}(2,\mathbb{C})$ spin chain, the eigenfunctions of the special matrix element of monodromy matrix are constructed. The key ingredients of the whole construction are local Yang-Baxter $\mathcal{R}$-operators, $Q$-operator and raising operators obtained by reduction from the $Q$-operator. The calculation of various scalar products and the proof of orthogonality are based on the properties of $Q$-operator and demonstrate its hidden role. The symmetry of eigenfunctions with respect to reflection of the spin variable $s \to 1-s$ is established. The Mellin-Barnes representation for eigenfunctions is derived and equivalence with initial coordinate representation is proved. The transformation from one representation to another is grounded on the application of $A$-type Gustafson integral generalized to the complex field. |
| title | A-Type Open ${\rm SL}(2,\mathbb{C})$ Spin Chain |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2507.09568 |