来自K-理论库仑分支的量子三角自旋Ruijsenaars-Schneider模型
Quantum Trigonometric Spin Ruijsenaars-Schneider Models from $K$-theoretic Coulomb Branches
AI总结：
本文利用4维N=2项链箭图规范理论的K-理论库仑分支，对N个粒子各带ℓ个自旋态的三角自旋Ruijsenaars-Schneider模型进行量子化，通过L-算子代数构造可积自旋链，推导了相关对易关系与运动方程。
AI中文摘要：
我们利用4维N=2箭图规范理论的K-理论库仑分支对经典模型的最新描述，对N个粒子各具有ℓ个自旋态的三角自旋Ruijsenaars-Schneider模型进行量子化，该4维N=2箭图规范理论对应具有ℓ个秩为N的节点的项链箭图。主要代数工具是由极小电荷的阿贝尔化单极算子导出的L-算子代数，它通过产生一族可交换哈密顿量，将项链箭图转化为可积自旋链。我们证明最低阶哈密顿量与K-理论库仑分支代数内部水平量子环代数量子行列式的第一模一致，其Bethe子代数生成极大可交换哈密顿量族。最后，我们推导了量子化物理自旋变量的对易关系和量子运动方程。
英文摘要：
We quantize the trigonometric spin Ruijsenaars-Schneider model of $N$ particles each with $\ell$ spin states using the recently developed description of the classical model in terms of the $K$-theoretic Coulomb branch of the 4d $\mathcal{N}=2$ quiver gauge theory for the necklace quiver with $\ell$ nodes of rank $N$. The main algebraic tool is an algebra of $L$-operators derived from abelianized monopole operators of minuscule charge, which turns the necklace quiver into an integrable spin chain by producing a family of commuting Hamiltonians. We show that the lowest Hamiltonian coincides with the first mode of the quantum determinant of the horizontal quantum loop algebra living inside the $K$-theoretic Coulomb branch algebra, whose Bethe subalgebra generates a maximal family of commuting Hamiltonians. Finally, we derive the commutation relations and quantum equations of motion of the quantized physical spin variables.
