Quantized Quiver Varieties and the Quantum Spin Ruijsenaars-Schneider Model
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908484408180736 |
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| author | Arutyunov, Gleb Hardi, Lukas |
| author_facet | Arutyunov, Gleb Hardi, Lukas |
| contents | This paper tackles the long-standing problem of quantizing the rational spin Ruijsenaars--Schneider model originating in the work of Krichever and Zabrodin. We make use of the technique of quantum Hamiltonian reduction to construct a quantized quiver variety $\mathfrak{A}_{N,\ell}$ associated to the framed Jordan quiver. This quantized quiver variety is simultaneously the algebra of quantum observables of the rational spin Ruijsenaars--Schneider model of $N$ particles with $\ell$ spin polarizations. Inside this algebra, we find a loop algebra and Yangian of $\mathfrak{gl}_\ell$ and conjecture that in the limit of infinitely many particles, the algebra $\mathfrak{A}_{N,\ell}$ becomes a shifted affine Yangian. We also exhibit a difference equation for eigenstates of the lowest Hamiltonian that reduces to the spinless case when $\ell=1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07862 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantized Quiver Varieties and the Quantum Spin Ruijsenaars-Schneider Model Arutyunov, Gleb Hardi, Lukas High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems This paper tackles the long-standing problem of quantizing the rational spin Ruijsenaars--Schneider model originating in the work of Krichever and Zabrodin. We make use of the technique of quantum Hamiltonian reduction to construct a quantized quiver variety $\mathfrak{A}_{N,\ell}$ associated to the framed Jordan quiver. This quantized quiver variety is simultaneously the algebra of quantum observables of the rational spin Ruijsenaars--Schneider model of $N$ particles with $\ell$ spin polarizations. Inside this algebra, we find a loop algebra and Yangian of $\mathfrak{gl}_\ell$ and conjecture that in the limit of infinitely many particles, the algebra $\mathfrak{A}_{N,\ell}$ becomes a shifted affine Yangian. We also exhibit a difference equation for eigenstates of the lowest Hamiltonian that reduces to the spinless case when $\ell=1$. |
| title | Quantized Quiver Varieties and the Quantum Spin Ruijsenaars-Schneider Model |
| topic | High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2508.07862 |