On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system
On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system
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三角自旋 Ruijsenaars-Schneider 系统的哈密顿公式
DOI：
10.1007/s11005-020-01320-x
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发表时间：
2020
影响因子：
1.2
通讯作者：
Chalykh O
中科院分区：
文献类型：
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作者：
Chalykh O
我们提出了三角情况下自旋 Ruijsenaars-Schneider 系统的哈密顿公式。在这种解释中，相空间是通过对框架乔丹箭袋的表示空间（的余切丛）执行准哈密尔顿约简来获得的。对于任意颤动，Crawley-Boevey 和 Shaw 引入了类似的变体，Van den Bergh 给出了它们作为准哈密尔顿商的解释。利用范登伯格的形式主义，我们在相空间上构造了交换哈密顿函数，并用自旋 Ruijsenaars-Schneider 系统识别了其中一个流。然后，我们计算局部坐标之间的所有泊松括号，从而回答 Arutyunov 和 Frolov 的老问题。我们还构建了一套完整的通勤哈密顿量并显式地整合了所有的流程。
We suggest a Hamiltonian formulation for the spin Ruijsenaars–Schneider system in the trigonometric case. Within this interpretation, the phase space is obtained by a quasi-Hamiltonian reduction performed on (the cotangent bundle to) a representation space of a framed Jordan quiver. For arbitrary quivers, analogous varieties were introduced by Crawley-Boevey and Shaw, and their interpretation as quasi-Hamiltonian quotients was given by Van den Bergh. Using Van den Bergh’s formalism, we construct commuting Hamiltonian functions on the phase space and identify one of the flows with the spin Ruijsenaars–Schneider system. We then calculate all the Poisson brackets between local coordinates, thus answering an old question of Arutyunov and Frolov. We also construct a complete set of commuting Hamiltonians and integrate all the flows explicitly.