负曲率黎曼对称空间的自旋Calogero模型
Spin Calogero models associated with Riemannian symmetric spaces of negative curvature
摘要：
研究了负曲率对称空间上测地线系统在任意动量映射下由等距群的极大紧子群约化的Hamilton对称性.限制在配置空间中的常规元素，减少一般产生一个自旋Calogero模型与双曲相互作用的对称空间的根系定义的潜力。这些模型配备了拉克斯对和许多运动常数，并可以集成的投影方法。在一定条件下对导致无自旋Calogero模型的动量映射的特殊值进行了分类，解释了Olshanetsky和Perelomov发现的具有两个独立耦合常数的$BC_n$模型与$SU(n+1,n)/S(U(n+1)\times U(n))$相关联的原因.在零曲率极限下，我们的模型再现了之前研究的有理自旋Calogero模型，并且类似的模型也对应于其他（仿射）对称空间。建筑工程也在量化水平。
英文摘要：
The Hamiltonian symmetry reduction of the geodesics system on a symmetric space of negative curvature by the maximal compact subgroup of the isometry group is investigated at an arbitrary value of the momentum map. Restricting to regular elements in the configuration space, the reduction generically yields a spin Calogero model with hyperbolic interaction potentials defined by the root system of the symmetric space. These models come equipped with Lax pairs and many constants of motion, and can be integrated by the projection method. The special values of the momentum map leading to spinless Calogero models are classified under some conditions, explaining why the $BC_n$ models with two independent coupling constants are associated with $SU(n+1,n)/S(U(n+1)\times U(n))$ as found by Olshanetsky and Perelomov. In the zero curvature limit our models reproduce rational spin Calogero models studied previously and similar models correspond to other (affine) symmetric spaces, too. The construction works at the quantized level as well.
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