标题： 广义Calogero模型在任意维度中的研究 显示英文标题

标题： Generalized Calogero model in arbitrary dimensions

摘要： 我们定义了一个新的D维多物种Calogero型模型，其中包含谐波、两体和三体相互作用。 利用潜在的共形SU(1,1)代数，我们指出如何找到Bargmann-Fock空间中的完整态集。 存在一系列状态，每个塔的状态具有等间距的能量谱。 我们明确构造了所有多项式本征态，即质心态和全局膨胀模式，并找到了它们对应的本征能量。 我们还为这些全局集体态构建了阶梯算符。 通过分析相应的Fock空间，我们检测到模型表现出奇异行为的普适临界点。 上述结果对于所有具有潜在共形SU(1,1)对称性的系统都是普适的。 显示英文摘要

摘要： We define a new multispecies model of Calogero type in D dimensions with harmonic, two-body and three-body interactions. Using the underlying conformal SU(1,1) algebra, we indicate how to find the complete set of the states in Bargmann-Fock space. There are towers of states, with equidistant energy spectra in each tower. We explicitely construct all polynomial eigenstates, namely the center-of-mass states and global dilatation modes, and find their corresponding eigenenergies. We also construct ladder operators for these global collective states. Analysing corresponding Fock space, we detect the universal critical point at which the model exhibits singular behavior. The above results are universal for all systems with underlying conformal SU(1,1) symmetry.